He struggles against Sheik. I'm a Sheik main, and I'm not being boastful, but I have never come across a Bowser that I have had trouble with as Sheik. Her grabs can lead into some great combos, working especially well against large, heavy characters. This applies to Ganondorf, Donkey Kong, and King Dedede as well.
On the flip side, I always have trouble against light charcters like Sonic and Jigglypuff.
Edit: He doesn't struggle against just Sheik, but characters who rely on grabs and fast combos to get kills. I meant to use Sheik as an example among other characters (Captain Falcon, possibly Sonic, Pikachu, Lucario, etc).