Never played anything before 7. Hated 7 with a passion. I guess I was frustrated cause I didn't really see all the hype that everyone was generating around it. People raving about it, I couldn't experience it that same feeling, I suppose. It just felt really bland.
8 Was probably the first one I got into fully, as a kid. It was an amazing experience for me, who didn't have much experience with the genre. Right after I played that, I spent time with FFT after seeing it in a magazine. One of my favorite games ever. FFTA and FFTA2 came after. I would play the hell out of a 3DS Final Fantasy Tactics. Perhaps Advance 3?
I briefly played 9, not enough to really give too in-depth of an opinion.
Played 10 inside, out, and backwards. One of my favorites. Didn't play 10-2 much, not enough to get into it at least.
12 was pretty amazing for me. It made me feel like I was playing an MMO at times, which I'd never played. Lots of fun things to do, marks and the like. Great system.
13, oh boy. I have a love-hate relationship with it. Well, a like-hate relationship with it. Coming off from 12, I expected it to be more of what 12 was. More like 12. I was excited. I enjoy open world roaming, I enjoy tons of sidequests, lots of hidden features...tons of content that I could be doing when I'm not working on the main quest...I got none of that from 13. It was almost non-existent. The story interested me, however. The battle system was...something that could have been a lot greater. I don't understand why the need for an autobattle button, and I kind of expected to be able to freely control my character and dodge AOE and attack manually.
Paradigm shifts were a good idea that I kind of liked, but it still seemed like a downgrade from 12 in every respect. I wanted to develop my characters and customize their skills, but the customization of skills in FF13 was so linear. And yeah, the game boasted a large amount of "paradigm combinations" but in the end, you only ever needed 6 sets. A set specifically for debuffing, one for healing. One for defense. Thanks to how paradigm stacking worked. If this game were 20 dollars, I would have liked it. But it was 60 when I bought it. I didn't get what I thought I was. I enjoyed the experience, but the game was one long cutscene. The open world was just moving between cutscenes. Even the battle was a cutscene. You could make it battle for you.
13-2: I tried to get into it. The whole time travelling nonsense confused me and my PS3 got sold before I could really finish the game. Or even get 25% in. (If even that.)
13-3: I haven't played it, but I'm curious to how it plays. The battle system looks a bit more like what I was hoping for, and I do like playing dress up. Maybe when it comes to steam and is hopefully 20 dollars.
TL;DR: I dunno that I'd prefer "old" or "New" ones myself. As some of the old ones I hated / haven't experienced, and some of the new ones suffer the same fate.