Are there any differences, beyond the visual ones, between the Nintendo Switch Pro Controller and its special editions, like the Super Smash Bros. Ultimate Edition?
If so, what are they?
There's no difference, besides the look. All Nintendo Switch Pro Controllers have the same exact functionality -- the only difference is that the Smash Ultimate version has a different look than the normal one.
They have different looks. I also heard that the xenoblade chronicles 2 one also has a better d-pad, it has a longer pole and other technical stuff which basically means you are less likely to press say, up and right at the same time while you wanted to press just up.
However I believe this also affects pro controllers that were manifactured after the xenoblade chronicles 2 one. I have a bland-gray-transparent one and I can't press all the dpad buttons at the same time.