In most cases, Pegasus Knights are great units. Their mobility allow them to pick off threats which are otherwise hardly reachable, bypass obstacles and attack units which would be otherwise difficult to hit because of a choke point. Almost all Pegasus Knights have very high Speed (and Luck) too, meaning they will almost never get doubled, and they will evade attacks from everyone easily (except Axe users). Finally, they usually have high Resistance, making them fantastic Mage killers.
They do come with flaws which can't be overlooked. They have low to poor Defense in general, same for their HP, and they really can't take too much hits from physical attacks. This flaw is exacerbated by their weakness to Bows, which deals 2 to 3 times more damages than usual against them. Depending of the game, they can also be weak to Wind magic (although that threat is lessened thanks to their high Resistance).
In some games, they can face issues because of the Weight of their weapons. Indeed, Lances can be very heavy weapons, and will impact severely the Pegasus Knight's speed if they use weapons too heavy for them. This is especially notable in the GBA games, in which one must be wary of using weapons which are too heavy for one unit's Constitution (Con)/Build stat. Pegasus Knights don't come with a very high Con stat usually, and as such using lances that hit harder but which are heavier will make their Speed drop to a very dangerous level, and allow enemies to double them in the worst case scenario.
Long story short: don't equip your Pegasus Knights with Steel Lances (Weight: 13), unless you know what you are doing. It will get them killed. I'm looking at you Fiora (Fire Emblem: The Blazing Sword, second pegasus knight you can recruit, who comes equipped with a Steel Lance when her Constitution stat is only 5, meaning she suffers from a -8 Speed penalty when using one).
On a side note, Iron Lances's weight stat is 8... meaning that even using the most basic lance will make your Pegasus Knights suffer from a speed penalty. It's a good thing they come with a high Speed stat upon recruitment and have high growths, otherwise they would be utterly useless in the GBA games.
The Constitution stat alone has a tremendous impact on how some units can perform in the GBA games. Most Cavaliers/Paladins in these games have a rather high Constitution stat, allowing them to wield Lances and Axes without suffering too much from a Speed penality.
And then you have Isadora, who is an already promoted unit with a Constitution of 6, whereas every single other Cavalier has at least 10 after promotion. Meaning that pretty much every single weapon will weight her down (yes, including most Swords, which are the lighter weapons of that game, aside from Tomes). It really rubbed me the wrong way that the sole female Paladin from that game was afflicted by such a huge handicap compared to her peers. She joins a little late too. Any of the base Cavalier will be way better than her if they are trained, with Kent surpassing her in pretty much every single stat except for Luck, and Sain will absolutely destroy anything in his path thanks to his insane Strenght growth. The only one who she could beat in offense would be Lowen, since that unit's particularity is his high defensive stats (for a Cavalier), and he has mediocre Strenght/Speed/Skill growths (he does have the best Constitution of all Cavaliers/Paladins, allowing him to use heavier weapons without a speed penalty, but that doesn't salvage his low offensive output).
