So would the 2.0 size be too narrow for my Cube Reaction Race? Would the 2.35 be better?
Well, as in most things bicycle related, much is personal preference and what's one mans meat is another mans poison!
However I have used 2.35 Big apples on my own Cube and they work and look great. I also currently have 2.0" ones on a hybrid bike of mine (that used to have 2.3 tyres) and while the 2" Apples work ok, I didn't think the slightly smaller size on paper would translate into such a puny looking tyre! I would have thought it might look a bit silly on a larger framed mountain bike.
I wouldn't risk it. Stick the big ones on if they fit (and they should on your bike)
I'd always go for bigger tyres if I can. The only caveat is that apart from frame clearance, you can run into squirm issues if your rims are a bit too narrow and the profile of the tyre type needs the wider rim to work properly. I'm not 100% sure on this though, but I have a feeling Big Apples are designated as a 'balloon tyre' and they seem to have a design that allows them to work ok on thinner rims.
hence 2.35" Apples seem to work ok on 19mm internal width rims, but I've run into issues with 2.35 G-One speeds on the same width rim (hence the reason I've dropped down to try the 2" Apples on my hybrid)