Wrath Of Khan and The Empire Strikes Back are the obvious answers, and I personally think the modern parallels line up the same ; Attack Of The Clones is superior to the rather rubbish The Phantom Menace and Into Darkness is better than the still-rather-good Star Trek. I actually think these days there is a growing trend with superhero/comic inspired films where everything is episodic and a follow-up is, by design, "bigger" than its predecessor, and usually I find if I enjoyed the first film and things haven't been tinkered with too much, the follow up is better. I feel that way of The Dark Knight, Iron Man 2, The Amazing Spider-Man 2 and others, and just as X-Men 2 was better than the first, if we consider Days Of Future Past to be a sequel to First Class, I personally think it's a better film.
I also consider Batman Returns to be better than Batman but I may be biased because of Michelle Pfeiffer's turn as Catwoman.