Quality shines above genre in the best of stuff really. I had avoided Persona for a long time because of what it is described as, seeing waifu wars on the internet, etc. It seemed like it was just some self-insert high school harem game with a JRPG dungeon crawler attached. And at some level that is exactly what it is, but it is just better than it sounds. Particularly 4 in my experience, but I also liked 3 a lot and am thinking about digging deeper.
-The Wildcard ability plays off the creepiness of self-insert, especially coupled with those ridiculous text scenes on level-up. Yes, your character can have many faces. Yes, it is implied that he has somewhat ulterior motives in getting close to people. Yes, Igor and the finer workings of social links are unknown to your friends. Etc. I try to play the guy as a consistent character, but I like that darker undertone to the dubious venture.
-Characters are actually charming beyond being tropes and trying to be that niche type of girl you can't resist. Yes there is a lot of trope and yes the girls are falling over themselves to get in your pants, but that's just not all it is. For every conversation I just skipped through on a second playthrough, there were many more I actually wanted to see again.
-There is a high attention to detail and the towns, again particularly 4 for me, feel very well-realized. They do setting very well, which is a large part of the central concept: take the epic JRPG and fold it into a small, tight setting.
-The games have a lot of identity and strong visual and aural direction. Sometimes it is very very ‘teenage’ or ‘anime,’ like the Evoker in Persona 3, but the games just have a strong, consistent sense of style and you can feel the heart behind it. Clearly the games have an artistic direction that is more than just ‘paint by numbers for the fans’ even when it is obviously going for them. As is clear from how I keep coming back to this, it means a lot to me, especially when what is pulled off is, in the end, a good product.
-The battles are engaging, with an interesting approach to weaknesses that doesn't always translate well to the bosses (save those mid-bosses in Persona 3, but some of those guys were just obnoxious and too tightly tuned (at least on FES hard, especially for no party control).
Basically, the games are well-crafted and competent and that goes a long way. To be fair, I don't hate anime or dating in games outright. I don't want to present myself as more hostile than I am. It is just that I have a low tolerance for skin-flint anime/dating sim. Maybe it is cute-to-make-you-melt or stylish-as-fuck at the time, but it leaves a bad after-taste. Persona didn't do that to me.