I feel a little bad about putting F-Zero here, even though I massively prefer X. Consider it filler until I get some better examples to populate this with.

I like how we think. https://www.backloggd.com/u/letshugbro/list/second-times-the-charm/

Stole a couple from Jim's list and swapped out F-Zero with a much more appropriate Nintendo example

The difference between Uncharted 1 and 2 is night and day.

Dynasty Warriors? Complete genre switch, but nobody's out here saying what a great fighting game DW1 is

I wouldn't call it an awful game but seemingly no reason to play diablo 1 anymore

Yeah, I like quite a few of these games, but it's the relative quality of the first sequel that's important.
I considered a few of the 94-96 PS1 games that got much lusher sequels on the console later on (Tekken, Ridge Racer, Jumping Flash, etc.) but I've got too much affection for those originals to include them on my list.

you missed Devil May Cry 2

Its weird to think that Dynasty Warriors was a fighting game...

This is about when number 2 is better than number 1. I'm not listing Devil May Cry, sorry.

It is better it's the best one dante is so good

Bless you.
No.

Zone of the Enders 2, Gravity Rush 2

I considered ZOE, but my personal feelings towards the game's atmosphere and Kiss Me Sunlights prevented me from including it in my nominations. I'm glad you mentioned it though, as I was probably just looking for someone to blame.

Some of these series are pretty niche and unpopular in general but this is speaking from within the fans' eyes:

-Akiba's Trip: Undead & Undressed (the first game's remaster was hated even by fans of the sequel when it was finally localized)
-Blue Reflection: Second Light (one of the most dramatic shifts for the positive I've ever seen a sequel take)
-Caligula Effect 2 (same as above)
-Crash Bandicoot 2 (not saying the first Crash is bad but it sure is hard to go back to afterwards)
-Hatsune Miku: Project Diva 2nd (added the ability to hit notes with the D-pad, Extreme difficulty, songs featuring Vocaloids other than Miku, Diva room, in general a bunch of features that became staples of the series)
-Hyperdimension Neptunia mk2 (again, speaking relatively, but the first game had a universally despised battle system which mk2 revamped into one more tolerable and hasn't been overhauled in the main series since)
-We Love Katamari (I know there are plenty of people that still like the original... but We Love really blows it out of the water)

I don't really have a strong opinion on any of these, but I'll include most of them out of goodwill. Unfortunately, I am an established Katamari Damacy loyalist.

- Sonic the Hedgehog, both Mega Drive and Master System versions.
- Sonic Adventure
- Half-Life
- Portal
- Donkey Kong Country

Just to name a few.

I think all of those are "good 2s" (never been much of a Sonic Adventure fan, but nonetheless), but I don't think they make the originals seem horrible to go back to. Sorry.

super mario land 2, sly 2, ace combat 2, elite beat agents (over osu tatakae ouendan), paper mario ttyd (that's controversial though), puyo puyo tsu, kururin paradise. maybe panzer dragoon zwei but i feel silly saying that considering i have only played the original and saga. i can clarify any of those picks if needed

Aahhh... a hotbed of suggestions. Kururin Paradise is really good, but I love Kuru Kuru Kururin too, and can't bring myself to include it. It's probably how much of a weeb I was when I first played it, but I couldn't warm to Elite Beat Agents the way I did with Ouendan (even if skipping the intros was a huge benefit to the game). Zwei's one I hear a lot, but I've only played the original and Orta, and I'd like a more informed stance before verifying. Can't argue with the others though. They're in.

MGS2 outshines MGS1 in probably every way imaginable but MGS1 is still fantastic, so not sure if it matches your criteria

@Huss Going to have a tough time convincing me on that one, sorry

Air Combat (Ace Combat 2), Kane & Lynch Dead Men (Dog Days) and DBZ Budokai Tenkaichi (Tenkaichi 2)

Were you divided on Smash Melee? In terms of both mechanical depth and content it's a cut above Smash 64 but Smash 64 isn't bad, just limited.

I really like both Super Smash Bros and Melee, but the second is a huge jump over the original. I think that's a good call.

Octopath Traveller 2, Assassin's Creed 2 (huge improvement), Jet Set Radio Future (JSR is dogshit, Future is glorious), Mafia 2 (remake notwithstanding, it was a vastly more interesting sequel)