To be honest, it depends on the genre. I don't need innovation in racing games, but it's very welcome in RPGs, for example.

Depends on where the series is at at the time; in the 2010s for instance Zelda was in need of innovation and reinvention, hence BOTW. On the flipside, if a series is still feeling fresh but has some rough edges, then refinement is needed.

It's possible to stray too far from what makes a series great by "innovating" in the wrong direction.

Both

Depending on the game/genre, you can get away with more refinement than innovation. Call of Duty doesn’t need innovation between games. Street Fighter or Forza Motorsport or Elder Scrolls should imho.

If I absolutely had to choose just one, then I'd have to go with innovation just for the sake of keeping things fresh, as it sucks when a series gets stuck in a rut and starts to feel stale.

Some of my favourite games are innovative sequels; Resident Evil 4, Super Mario Galaxy, Breath of the Wild...

I do also appreciate refinement though when done right.

Yes

For me this question is a bit too vague (not knocking the OP as I like the topic) but it depends on what stage you are in with the series for me. If it's a new series and you're getting a first sequel I would say go for refinement all the way to improve upon what they made but to also define the series.

However when it came to the Zelda I think Breath of the Wild was the perfectly innovative title for that franchise at the time. I'm personally someone who wants to see Zelda go to its more traditional dungeon crawler roots again but I cannot deny that they needed to shake up the franchise.

If i was forced to answer the question above I would probably say innovate to any long-standing series but for young franchises refinement is far more important.

To often have I been disappointed in sequels changing things to much. I rather make new IPs if the core is changed. Innovate inside what made the previous installments great - what I would call refine.

It depends on if it is an attempt at re-booting a franchise or just a direct sequel to an established game.

Case in point, Super Mario Galaxy took a well established franchise and imo, turned it on its head with a brand new setting and gameplay mechanic.  Then that concept was further refined and made even better in the 2nd installment.  I feel the same is evident in BoTW and TotK.

I don't feel that a franchise needs a complete re-imagining every release, refinements are perfectly fine.  Eventually though, as good as a well polished game concept can be, without a re-imagining, it will eventually get stale and lose its lustre.  (NewSMB anyone?)