My preference is definitely the full freedom of three dimensional movement, but I don't think it's a good idea to force that on the player where it's not appropriate. Space games on a plane can be good too. Drifter is a recent release that does this pretty well.
Sound like you mean a Starfox type of gameplay.
Depends on the game and what else can be done in it, never played that many Shmup be they 3D or 2D.
The space mission sequences in Star Wars: The Old Republic are quite arcade-y, in that you're essentially a "ship on rails" and can only go where the screen takes you. It's still quite enjoyable though.
I think it will depend on what your target market is. If you're aiming to please hardcore space-sim fans, limiting movement will be seen by them as less realistic and they're not likely to want to play. But if you're after a more casual gaming crowd, it will make it easier to control and thus more fun.
auryx
You look good through a crosshair.
This would definitely not appeal to me, unless somehow it is compensated for by extremely interesting game mechanics elsewhere (for example, I remain very interested in To be worth playing, I think the RPG (or other, possibly strategy?) elements of such a game would have to be pretty impressive.
It's odd how "space" games has sort of become a genre since the kickstarter era, but I think one of the appeals of "space" is large numbers of degrees of freedom. There aren't enough games with the desired 6 degrees of freedom as it is, so it seems a little odd to go in the opposite directions.
If the idea is to pursue a genre other than a space sim though (RPG, strategy), it might have some appeal.