For the most part, wyvern riders are a big staple of the armies of the antagonistic/"evil" kingdoms, from Medon, to Thracia, to Daein, to Bern, to Nohr and all of that, while Pegasus Knights are normally used by the "good" kingdoms like Talys, Crimea, Hoshido, and all of that.The dragon riders even tend to be wearing darker armor than the pegasus riders, and they're usually riding dark-colored dragons. It's all design.
I'm not saying that the entire kingdoms are evil or everyone within them are evil, but that's how they're portrayed in-narrative. We get lots of allied units from the "evil countries," with Haar and Jill being the standouts in my mind, considering how often I've played RD and POR. In fact, RD changed things up a lot, putting the central focus on the "evil" kingdom from the previous game, to the point that you have to fight for its freedom. In an FE context, that was mind-blowing, and doesn't get as much recognition as it deserves, due to RD being controversial in a lot of aspects.