Though we all know that most sequels can’t hold a candle to the original film, I’m curious to hear some opinions on sequels that matched or surpassed the original. And, as a safeguard against repetition, let’s eliminate any Star Wars films, Indiana Jones films, or Wrath of Khan. My personal favorite is 2010. Better plot, better acting, better ending.
Aliens was better than Alien.
T2 was better than The Terminator
Although I haven’t seen it yet, I’ve heard that Shrek 2 was better than Shrek.
Most critics felt that Spiderman 2 was better than Spiderman.
The Godfather Part II was arguably better than the original. They were, of course, both Best Picture winners.
Superman 2
I thought Come Back, Charleston Blue was more entertaining than Cotton Comes to Harlem.
Gremlins 2 and X-Men 2.
Dawn of the Dead was better than Night of the Living dead of the Dead.
I think A Shot in the Dark is better than The Pink Panther. And how about Bride of Frankenstein over Frankenstein? Also, Drunken Master 2 is superior to Drunken Master.
Aliens
Terminator 2
X Men 2
Spider-Man 2
Oh, and despite your ground-rules, The Wrath of Khan. 
Back to the Future 2 was better than the first or the third, IMHO.
Same for Austin Powers 2
Some might disagree, but I thought that Babe: Pig in the City was better than Babe. Loved both of 'em, though.
Toy Story 2.
I adored Toy Story, and TS2 blew me away.
Army of Darkness (technically Evil Dead 3) is way better than Evil Dead 1 or 2, and 2 is better than 1.
I agree on X-Men 2 and Spider-Man 2, and I’d also like to add Blade 2–so far superior to the original.
Just about everyone agrees that The Road Warrior is a much better movie than Mad Max.
Well, I for one don’t agree - but that’s an Australian thing and I am part of that generation fo young australian men for whom Mad Max was a rite of passage, a religious artefact.
Back to the OP, I think The Two Jakes was better than Chinatown. Once again, I’m probably in a club of one :)…
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I dunno if I’d say it was better, but BTTF2 definitely kept the same level of quality from the other movies, IMO.
I pretty much agree with you.
You must see Shrek 2. Watch for the pepper grinders - it’s hysterical.
I don’t know about “just about everyone”, but to this guy, The Road Warrior is iconic (if I am using that term correctly).
Personally I thought the best Rocky was number 4 so that is better than 3 of its predecessors. Rocky 5 sucked shit.
For what it’s worth, comic book writer James Robinson agrees with you on that.