This one is tough, in that neither is Portal. The stories for both are simple, especially for RPGs, a genre famous for it's overly complex narratives. Paper Mario 64's story: Bowser has stolen the Star Rod, the tool used by the Star Spirits to grant the wishes of everybody. By stealing the Star Rod and imprisoning the Star Spirits, he is able to grant his own wishes, making him invisible. After thoroughly trashing Mario and kidnapping Princess Peach, Mario must free the Star Spirits, for only their combined might can oppose the Koopa King now. Pretty simple. Now, besides the main plot, each game has a second, separate plot where Peach is the main character. In 64, Peach befriends a tiny star named Twink. Over the course of the game, she sneaks around and uses what information she can find to give to Twink, who think informs Mario so he knows where to go next.
Paper Mario: The Thousand Year Door takes place not in the typical setting, the Mushroom Kingdom, but in the port town of Rogueport. One day, as a stop on a larger voyage, Peach and Toadworth (her loyal retainer) stay there for a while. While there, Peach finds a map that is supposedly magic, and leads to the legendary treasure said to reside under Rogueport. She sends the map to Mario, but when he arrives she is nowhere to be found. It turns out the map shows the locations of the Crystal Stars, seven artifacts that are powerful alone, but when combined open the Thousand Year Door, which is said to have the previously mentioned treasure locked beyond. Mario is not the only one looking for the stars, a group called the X-Nauts are looking too, and captured Peach. Peach's story in this game involves her growing relationship with the X-Naut's computer TEC. Bowser has his own side story as well, where he hears Peach was kidnapped by someone besides himself. He goes on a quest to find the Crystal Stars as well, but is always one step behind Mario.
The question of which main story is better depends on the answerer. To those who prefer more simple stories, 64 would seem the right answer. But for me, the main story of Thousand Year Door is much better. There's an actual twist to it, and the plot has more twists. I'd say that Peach's story is much better in Door as well. Her relationship with TEC is very well done, and by the end it's actually very touching. Plus, Door also has the Bowser subplot, for which there is no opposite in 64. So, for me, Door is the clear winner here.
WINNER-Paper Mario: The Thousand Year Door
This one is really, really easy. I'll just list all the things that Door did better: start with action commands, and you can skip the tutorials; audience; more skill involved in the special moves; better badge system; better partner system; paper curses; appeal and defense options. The only thing 64 had that Door didn't was the spin thing, which I do miss, but even considering that loss Door still is the easy winner.
WINNER-Paper Mario: The Thousand Year Door
Another tough one, we'll go step by step to see which is the victor here.
In the prologue for 64, Mario goes to a party as Peach's castle, Bowser shows up, kicks Mario's flank, Mario wakes up in Goomba Village, gets a hammer, gets a partner, fights the Goomba King, goes to Toad Town, goes to Shooting Star Summit, finally learns action commands, reveals the trickery of the Koopa Bros, and finally heads off to Chapter One.
In the prologue for Door, Mario gets off the boat, already knows action commands, fights Lord Crump, gets a partner, gets robbed, gets cursed, and learns where the first Crystal Star is.
On the one hand, 64 has a long and interesting prologue. On the other, the combat sucks until near the end. Still, I'll give this one up to 64.
In Chapter 1 of 64, Mario finds the Koopa village overrun by fuzzies, defeats them, gets a partner, attacks the Koopa Bros. Fortress, gets another partner, fights a fake Bowser, fights the Koopa Bros, and then gets the Star Spirit.
In Chapter 1 of Door, Mario discovers that a dragon named Hooktail is terrorizing Petal Meadows, wins a quiz show, fights a gold fuzzy, gets the keys to the castle, gets a partner, storms said castle, gets cursed, fights the dragon, and gets the first Crystal Star.
This one is tough. Door has the cool castle, the better puzzles, and a cool midboss. However, 64 has two different partners, some really funny moments, some very awesome moments, and overall feels more complete and satisfying. I'll give this one to 64 as well.
In Chapter 2 of 64, Mario rides a train, gets a partner, (optionally) fights a giant buzzard, goes into the desert, finds a mysterious mouse who knows where the ruins are, find the ruins, gets threatened by a lame voice, gets the Super Hammer, fights a koopa dressed as a pharoh commanding Chain Chomps, and gets the Star Spirit.
In Chapter 2 of Door, Mario befriends this little slug thing, goes into these black and white woods, tries to enter The Great Tree, fights the Shadow Sirens gets a partner, enters The Great Tree, has 10 more slug things join him, gets 90 more slug things to join him, gets the Super Boots, almost gets the Crystal Star until Crump steals it, fights Crump in a mech, and gets the Crystal Star.
Door tried doing a lot of interesting things. The woods were an interesting style choice, the Punie's following you was something new, the stealing of the star and subsequent countdown timer was new, and the mech for a boss fight was different. However, I don't feel most of that really worked. I'm glad they tried new things, but despite that 64's simple search for the ruins, and the questing within, was far more memorable and fun. 64 wins again.
In Chapter 3 of 64, Mario goes into a haunted forest, goes into a haunted mansion, gets the Super Boots, discovers that the Star Spirit has been stolen from Bowser's henchman already by the Boos, works out a deal to get rid of the Tubba Blubba in exchange for the Star Spirit, gets a new partner, goes in Blubba's fortress, sneaks around cause he's invincible, find out his secret, races to avoid Blubba's wrath, finds his secret, defeats Blubba, and gets the Star Spirit.
In Chapter 3 of Door, Mario goes to a floating city, discovers the Crystal Star on the belt of the champion wrestler, becomes a wrestler, gets a partner, works on the secret of this place, gets the Super Hammer, title fights the champ, defeats the bad guy abusing the Star's power, and gets the Crystal Star.
I am going to preface my decision with this: chapter 3 of 64 is one of my favorites of the game. It takes many risks, and pulls them all off perfectly. It is a great chapter, and I'll never say a bad word about it. However, I find Door's Chapter 3 superior. It takes an even bigger departure from the formula, has a lot of great jokes, and delivers a far more memorable experience. I'm giving this one to Door.
In Chapter 4 of 64 (RHYMING), Mario find Toad Town under attack by a legion of thieving Shy Guys, finds their base, bakes a cake for the Gourmet Guy, defeats the Lamp Ghost, gets a partner, defeats the General Guy, and gets the Star Spirit.
In Chapter 4 of Door (MOAR RHYMING), Mario goes to Twilight Town, discovers that when the nearby Steaple's clock goes off someone turns into a pig, gets cursed, (optionally) fights an Atomic Boo, fights ??????, and gets the Crystal Star...except not. Mario then is turned into a shadow while ?????? has taken his name and body as well as his partners, gets a new partner, learns ??????'s name, fights ?????? and his old partners, and gets his body back as well as the Crystal Star.
Again I preface my decision by saying that I love 64's Chapter 4. I love the Shy Guys, the many different variants, the fun in getting everybody's items back, all of it. But Door took more risks, and they all worked for me. It's a really fun chapter, so I'll give this battle to Door.
In Chapter 5 of 64, Mario rides a whale to Yoshi's Island (It's
not might be the one you're thinking of.), finds that the Yoshi's children have gone missing, gets a new partner, saves all the kids, meets that giant raven from Super Mario World 2, gets into a volcano, gets the Ultra Hammer, fights Lava Piranha, fights Lava Piranha on fire, barely escapes the exploding volcano, and gets the Crystal Star.
In Chapter 5 of Door, Mario rides a ship to an island, crashes into said island, gets a partner, goes into a cave, gets cursed, fights a pirate ghost, gets the Crystal Star, and fights Crump again.
This one is tough, partially because they're very similar. On the one hand, I really like the Lava Piranha fight, and the escaping the volcano run. On the other, the Cortez fight is really interesting. Still, I got to give it to the 64.
In Chapter 6 of 64, Mario goes into this weird alternate world full of plants, gets some items, gets a partner, gets Ultra Boots, clears up the sky, grows a giant beanstalk, fights Huff 'n Puff, and gets the Star Spirit.
In Chapter 6 of Door, Mario rides a nice train, solves a mystery, gets Ultra Boots, fixes the rails, fights Smorg, goes into a painting, and gets the Crystal Star.
Which you prefer really depends on what you like in the game. For those who prefer the combat, 64 is the clear winner, because Door barely even has any. But for those like me, Door barely eeks out a victory. The fun with the passengers is great, the baddy is interesting and weird, and it's very different experience.
In Chapter 7 of 64, Mario goes to Shiver City, solves a mystery, goes to the birthplace of stars, goes to the Ice Palace, fights the Ice King, and gets the last Star Spirit.
In Chapter 7 of 64, Mario goes to Fahr Outpost, goes around convincing Bob-Ombs to reactivate the cannon, gets shot to the Moon, invades the X-Naut base, fights Crump, gets the last Crystal Star meets a dying TEC, and escapes just before the base explodes.
This one is a clear victory for Door. It has more locations, more epic scenes, and the X-Naut base is very cool.
In Chapter 8 of 64, Mario climbs the Rainbow Way, receives the blessing of the Star Spirits, invades Bowser's Castle, invades Peach's castle, fights Bowser, and saves Peach. The End.
In Chapter 8 of Door, Mario opens the Thousand Year Door, fights Gloomtail, fights Grodus, fights Bowser, fights the end boss, and saves the world. The End.
This one is close. Door has more boss fights, but the general build up and excitement in 64 is better. Giving this last one to 64.
So, for the chapters,
WINNER-Paper Mario 64
No pics this time, no time.
Goombario VS Goombella: Goombario is...okay I guess, but Goombella has far more personality, and I prefer her by a ton.
Kooper VS Koops: This is another easy one. Koops at least has some personality, so he wins.
Bombette VS Bombery: I guess Bombette had some personality, like I think she was Tsundere or something, but Bombery's old sea dog thing is way better.
Bow VS Vivian: I really like Vivian and her story, but Bow is too awesome not to win.
Watt VS Flurrie: Watt is adorable and Flurrie is...annoying and disturbing. Watt wins.
Sushie VS Ms. Mowz: Sushie had some character traits, but Mowz was well set up, interesting, and fun. Mowz wins.
Spike VS [Insert Chosen Yoshi Name]: The Yoshi is cool, with different colors and a custom name, but I found him a tad annoying, and I really like Spike. Spike wins.
Koopa Troopa Jr VS the Shadow Sirens: Junior appears far more often, is more funny, and has a far sillier motivation. Mario walked around in his playground, so he follows him across the Kingdom, ignoring anything that can stop him, and slowly becomes a total badass, just for revenge. Awesome.
Koopa Brothers VS Hooktail: Hooktail is a dragon, but has a really lame weakness. The brothers have an awesome theme, funny dialogue, and a hilariously bad Bowser Costume. They win easy.
Tubba Blubba VS Grubba: Tubba is more funny, pathetic, and has a more interesting story. He wins.
General Guy VS ??????: I really like General Guy, but he had little screentime. ?????? had more, and was more interesting overall. Mystery monster wins.
Lava Piranha VS Cortez: Cortez is cool and all, but the Lava Piranha blows him outta the park. LP wins.
Huff 'N Puff VS Smorg: Puff is cooler, funnier, and while not as mysterious, far more infuriating when you're a kid. Puff wins.
Bowser VS Grodus: Grodus is generic, while Bowser is fun in his evilness. Koopa King reigns supreme.
Kammy Koopa VS Crump: Kammy. Nough said.
Twink VS TEC: Twink had no personality. TEC's story made me cry. Do the math.
Add it all up and...
WINNER-Paper Mario 64
This one won't take long. 64 expanded and filled the Mushroom Kingdom, giving a better identity to a place we had vaguely seen in other games. Door gave us the town of Rogueport and the surrounding areas. I prefer that of Door, because it shows that the world of Mario isn't all a paradise, and bad places exist. It also did far more world-building, which is always a plus for me.
WINNER-Paper Mario: The Thousand Year Door
Well, I guess Thousand Year Door wins. This does not mean I don't love Paper Mario, it just means that I think the sequel is one of the rare few that surpasses the original. Laters.