Can also specify the below to help people answer your questions;

34" Ultrawide Curved - there are 2560x1080 and 3440x1440 I believe, which resolution?
32" Monitor - 2560x1440 resolution or 1920x1080?

There is cross-relevance to my question when attempting to answer/consider your gaming concern, since I can strongly recommend you a 34" 3440x1440 curved ultrawide for really immersive gaming experience but your GTX980 might struggle to drive that resolution. If you answered me 34" curved ultrawide 2560x1080 then I would recommend to go for it and select monitor such as Acer Z35 or LG 34uc79. I didn't ask irrelevant question bro

Since you did rate movies, web browsing (and assuming other productivity-type applications) as your higher focus at 60% then 34" curved ultrawide will still offer you a better experience imho, regardless of resolution.

If you want to be able to game as well at decent settings, then 34" curved ultrawide 2560x1080 (assuming you continue to use GTX980 as your GPU) OR you can go with a 32" 1920x1080 or 2560x1440 (I used a 980 to game at 2560x1440 high settings, no problem).

4K, a different can of worms here. Your 980 will shit bricks trying to drive 4K gaming at high to ultra settings. Might get away with medium settings on some recent to older titles, not sure. However with your 980 surely you can handle all other usage needs on a 4K display such as movies, browsing, etc.

My point is, your initial question was simple but the answer to them is not as straight-forward.

I upgraded from a 27" 16:9 2560x1440 monitor to the Predator x34a (34" 21:9 3440x1440). Not one ounce of regret and definitely never going back to non-ultrawide

GL with your choice bro.