1 and 2 are old school JRPGs, dungeon crawlers (the first even having a first person perspective) without the social sim perspective. However, they do have very good characters and stories (especially the Persona 2 Duology), excellent music (1's original soundtrack is incredibly atmospheric) and at their core, fun gameplay.

However, they suffer from jank issues and high encounter rates, not unusual for 90s RPGs. Persona 1 had a remake for the PSP that unfortunately changed the soundtrack to one I consider inferior. 2 (Innocent Sin)'s PSP port is bad due to it messing up the difficulty and making the game way too easy. Eternal Punishment's fixes that but has the issue of being a sequel game and not reaching the same heights as its predecessor. Still highly worth playing imo.

Persona 3 has a lot of versions and unfortunately none of them is the ultimate version to play it. The new remake is probably the best one, but Persona 3 Portable (with its half assed PC port) has an entirely new route, that of the female protagonist.

3 introduces the social simulation aspect of the game, and has the unfortunate issue of being very slow in the beginning. Once the story gets going however, it becomes really good and the best written and most mature of the new Persona games.

Persona 4 is known for being far lighter in tone for the most part, having a memorable rural setting and character cast. The villain is really good, but the additions of the "Golden" re-release are kinda bad in quality in my opinion. The game really ups the anime-ness of it all in ways that have not really aged well. The game is also dragged down by its clearly right wing, socially conservative writing that shines through in many aspects unfortunately.

Persona 5 is very stylish. Set in Tokyo, it takes on a revolutionary/rebellious aesthetic and some of the themes it tackles are very interesting and challenging assumptions in society. While ultimately liberal in writing, it fails on a different way - it feels very stitched together at times, only finding sure footing at the final third of the story. The gameplay is very sleek and fun, though some would call it a bit too easy. Definitely not as bad as Persona 2: Innocent Sin however. The one big issue is that the game is LONG. Somewhat bloated, in fact. And weeb-brained, like Persona 4 is.