I'd imagine that Falcon would be harder to combo with. His usmash/uair combos work fine on flat ground at first, but to extend it past a few hits you usually need platforms.
Fox's laser game would definitely improve as it does in Melee. However, I suspect one of his easy finishers, the uair, would be less useful. There are two ways to insure an easy kill with uair. The first is when the opponent strikes a wall, such as in the **** tent on Hyrule. The other is when opponents are bouncing around on platforms, as it's easy to just stay on the bottom, wait for an opening, and uair ftw. Neither be possible on FD.
I suspect that pikachu's recovery game would also hurt on FD. One of pikachu's strengths is that with his two-direction Up+B, it's very easy to accurately hit any of the available options: edge, stage, platform. Even an open area like the left side of Hyrule has options: edge, near stage, mid stage to try to use the wall for protection, and far stage past the little wall to force the opponent to jump, slowing him down. FD has only two options, edge and stage. Not many opportunities for mindgames there.
What about mario's fireballs? I'm not that experienced with mario, so I'm not really sure if the lack of platforms would help or hurt his projectile game.