I liked both. I liked the vs. thing WK did so I'm gonna do my own extremely simplified version.

Setting: I love a good fantasy world created through imagination and left apart from reality. Hands down, this goes to XIII. Pulse and Cocoon have so much going for them, while a "Fantasy based on Reality" just ended up meaning "A lot of boring stuff" for me. I loved the place inspired by Venice, though.

Plot: Eh, not fussed either way. Probably FFXV.

Cast: XIII. Some characters I didn't like at the start I ended up loving, and that's impressive. Granted, there were still characters I didn't care for over the long run but I really enjoyed others, and it felt very Final Fantasy VII in some ways for me as the characters had a lot of variety to them, a lot of clear purposes or driving factors... a lot of character! I liked pretty much everyone in FFXV too but I didn't love any in particular, which left them running behind on this one.

Villains: Definitely preferring FFXV on this one. FFXIII's villains were bland sideplots to me. If we count the later games, Caius was cool.

Combat Systems: I suppose I probably preferred FFXIII, but battle systems are rarely the important thing for me in a Final Fantasy game. I just want to feel immersed in the characters and world. I do at least commend the games for giving me far more of a challenge than I ever experienced in the previous games in the FF series (MMOs excepted) because I actually had to think in a lot more battles than in, say, FFVII where I could generally get by holding down buttons to win at the fastest speed possible, even against bosses. Not being able to overlevel in XIII (I forget if I could in XV) meant I had to be careful at times, and learn the right paradigms. I liked the idea of the star systems for your battles too, so you could find the most efficient ways to win against various enemies over time.

Sidequests & Minigames: Oh, FFXV. Not even a contest. The FFXIII Cie'th stones were better than the Mark Hunts in XV but fishing alone stomped XIII into the ground when it came to minigames and sidequests, because quite frankly aside from Cie'th stones in XIII there are no sidequests or minigames. Basically in XIII there was nothing to do at all other than battle and do story stuff. At all. Okay, you could do chocobo digging thing but that wasn't really worth the time and it wasn't entertaining either.

Soundtracks: Probably FFXIII. I remember a lot of songs over the XIII series, and little to none of the XV game. Not a slant to XV at all which had good music, but XIII was good and had memorable songs.

Art Direction: XIII, for reasons explained well by WK. I like the colourful nature of it all. It works well for my desire to experience fantasy over reality.

Sequels vs. DLC: Can't comment on the FFXV DLC as I didn't play it, but I really enjoyed the different natures of the various FFXIII games because they were actually different while still being similar enough to be connected. FFXIII-2 and LR:FFXIII weren't a saving grace to the plot of FFXIII by any means, but they addressed the gameplay issues fantastically and I really appreciate the later entries for this. It showed experimentation by Square-Enix, something I feel they sorely needed to do.