I can't speak for SMT2, but I wouldn't really know how it's like FFX. It's not that different from SOUL HACKERS, except you have more control over your party (at least SOUL HACKERS isn't as bad as the original DEVIL SUMMONER was in terms of punishing you for attempting to select your own moves). You pick the moves for your entire party, and then stats determine who goes first.
I haven't played the original Devil Summoner, so I can't comment on it. Persona 2's got that system where you can adjust the turn order and all, in a manner similar to FFX's turn order bar. Heck, they even added the aformentioned bar to the PSP remakes. =P
I forced myself to beat it, but I found the dungeons so horribly bland that it often felt like a chore. The fact that their Sega Saturn game released the same year (I think) had more sophisticated graphics says a lot about the effort that went into Persona.
Well, it seems Persona was kind of an experiment of sorts, and one that didn't pay off until Persona 3 years later.