This is a question which I’m torn over— Would you rather have a Super Mario Sunshine (a sequel in all-but-name to SM64) or a Super Mario Galaxy 2? Would you rather have a Super Mario Bros 2 JP or Super Mario Bros 2 USA? Would you rather have had a more traditional follow up to Super Mario World than Yoshi’s Island? What about Bellabel Park versus Bowser’s Fury?

And looking beyond Mario: What about Halo 2? Would you have wanted a Pikmin 2 or a Pikmin 3 as the follow up to Pikmin 1? Luigi’s Mansions 2? NS2 (keep the good times coming!) or Wii U (innovate with a gamepad controller)?

No prefference, it just needs to be a good game.

God of War 2 was more of what 1 was and it was great.
4 was completely different from 3 and it was great as well.

I typically lean towards innovation, or at least introducing something new that makes it truly feel like a sequel. I don't typically care much for more of the same or get the feeling like I've played this game before even though it's technically new. Would've been fine 20 years ago when we were getting entire trilogies within several years, but in the age where it takes nearly a decade to get a new game, getting more of the same just doesn't feel as good to play after waiting that long.

Yeah, I agree with @BraLoD 

Neither innovation nor refinement are inherently good. It's all relative. If the premier game is crummy, I'd want them to innovate and move away from what didn't work. If the premier game is fantastic, then I'd want them to build on that foundation. But even beyond that, sometimes a sequel that moves far away from a brilliant foundation is just as great — only in a different way.

Innovation implies creating something new. I will rephrase your question as: You want changes or refinements?

There is not a fixed rule, however there are situations where I specifically want and expect some sequel to change or to refine

- I always want changes when the formula is either flawed to the core, stale/outdated or overused by other games that did better job

Exemple: Dragon Quest (stale), Assassin's Creed (overused) and Starfield (good in concept by flawed in game design or lack of thereof)


I want incremental evolution when

a) The game has overall good structure and design but the systems feel too simply and lacking depth
b) When they found the right gameplay concept but did quite delivered it to its full potential
c) or when the mechanics are very niche/unique with very few similar offerings in the market

Exemple:

a) Final Fantasy XV. Combat gameplay flows nicely and is fun to play, but it's too shallow. It needs more RPG elements and more tactical use of teleport. I like the semi open world and day/night structure of the game, it just needed more depth
b) Octopath Travaler 0. I like the concept of controlling the 8 party members, but the game faces severe balancing, passing and structure issues derivatived by the fact your characters have almost no personality or presence in story (you only get the characters plot-relevant really late). They can keep the combat mechanics, but they need to fix those problems
c) X Com. There is simply very few tactical games that plays like X Com, even if I'm not the biggest fan of some of its randomized structure I'd rather keep X Com as its own thing instead of turning it similar to another tactical combat game

I want innovation from a sequel. For refinements I would prefer an expansion/DLC,

I dont prefer one over the other, both work well for me.

FF7 remake builds over the OG game and adds to the story - and at times deviates from the story. And i like both games quite a lot cause they made them so well.
But had they done the exact same OG game, just with added QOL features, and a gaphic upgrade (maybe HD2D) i wouldve liked it as much if its well done.

Final Fantasy reinvents itself completely with ever new entry, and that great. Dragon Quest keeps the same formula with every new entry, just adds more qol feature and a bith more depth to it, and thats also great. Both concepts work when they are well done. 

Depends entirely on the game. Honestly generally not much preference. ZOE2 takes what works in ZOE1 and refines it. Takes what didn't work and rethinks it. SF1-II innovated an entire genre. It's a case by case basis.

Innovation. Always.

A healthy mix of both, with varying proportions, is probably a good recipe. If you stray too far due to innovation, might as well not call it a sequel, but stay too close to the previous game, and might as well not make a sequel. Of course 'too far' and 'too close' are not well defined, and they do indeed probably depend on the game as well.