@dagda The worst part about Persona, in my opinion is the 'One more' system. Weaknesses now increase damage dealt and allow to execute an extra turn is a weakness is exploited in an enemy. Since you have 3 extra teammates and 6 Persona (demon) slots to start with, this becomes extremely easy to plan for any weakness and get a bullshit extra turn. You also can't lose control of the battle like you can in SMT. The Press Turn system from SMT mogs it and it's not even close. That being said, One more isn't *that* bad and it can be satisfying to play.
Persona 1 is by far the most similar to SMT. It's alright but the persona fusing is annoying, some weird card system. Also the PS1 version, which has an official English translation, features odd changes, like a whole route being cut, as well as one of the characters is made black. If you're gonna play it, play the PSP version, even though it makes all the music J-Pop instead of the original's more standard SMT soundtrack.
Can't comment on Innocent Sin, nor Eternal Punishment because I haven't played enough of them. What I have played of Innocent Sin is fine.
Persona 3 is probably the most unique because in the PS2 version you can't control your party members beyond giving them vague directions (I.E, play defensive, play aggressive). Also the one that 'ruined' the series in purists eyes, adding all the modern Persona stuff, like the calendar, dating, social links, etc. I honestly like all that crap, it gives the game an interesting flow.
Persona 4 is my favourite and the one I've by far played the most, and you can actually control your party members. This one is easier than Persona 3, and way easier than most of the SMT games. There's also no infinite grind dungeon in this one, it's the only one of the 3 new Persona games not to feature an infinite grinding dungeon. The only hard parts are a few of the bosses. I can only really think of three that gave me trouble. The story in this one is the most fun, in my opinion, and has the most likeable romance options. It also has the most fun villain, if you haven't been spoiled on them already (which you probably have).
Persona 5 is by far the best in terms of presentation, not only of any SMT game, it's probably one of the best games of all time in terms of presentation. That being said the story is shit and the game is piss easy, though it drags on for fucking ever. It took me about 110 hours to beat the game, if memory serves me right. And that definitely wasn't mostly combat. The bosses are piss easy, and the hardest boss is probably the first one just because you're so low level. The bosses basically one by one get easier. I think I beat both the final boss and the true final boss on my second try. It's still probably worth playing, but it's not the most satisfying if you're even vaguely decent at JRPG's.
If you only played one of them to try, I'd probably recommend one of the new ones, to be honest. Persona 1 is really nothing special in my opinion, it's a fairly standard SMT spin-off. You'll get a more novel experience playing 3, 4 or 5.
My heart says I'd recommend Persona 3 FES because it's by far the most novel and interesting in it's mechanics, but it's honestly not that gripping as you start playing. By comparison, Persona 4 gripped me pretty quickly. And the fact you can control your party members will cause less frustration.