When I look at the modern representatives of synapsids and sauropsids respectively(mammals versus birds and reptiles), the difference in species seems trememendous. What were some of the causes for this difference in diversity? While I'm guessing that the Permian-Triassic extinction was likely a major factor, I'm wondering if there were other causes.

I suppose it depends on your definition of diversity. I would argue that the living synapsids (mammals) are actually more diverse than the living sauropsids. There are mammalian species in pretty much every form including flying (bats), aquatic (cetaceans), arboreal (primates), and so on.