Comparing between XIII and XV:
XV Better:
~ Characters - I liked the bros a lot better than anyone in XIII, Aranea was great for what little she was in, Iris and Cindy were both unoffensive (you know, outside of Cindy's design) and Ardyn was fantastic. I really didn't like many of the characters in XIII outside of Fang, Sazh and Snow (yes, I kind of liked Snow!)
~ Enemy design - The monster designs and modelling in this game (I'm also including summons here) were fantastic. The closest to polygonal Amano art yet. Those Ronin and Goblins man...
~ Level/World/Dungeon design - XIII was way too linear and while it had a cool look to it with it's cyber future fantasy stuff I just prefer what we got from XV. Altissa was beautiful even though it was just hyper Venice, Lestallum made me think of Midgar with its powerplant and more working class streets and market, Insomnia (the little we saw) was great and I loved how it was basically Tokyo complete with a bunch of Japanese everywhere which added to how different the crown city is from the rest of Lucis. Plus the dungeons had their branching and criss-crossing pathways and Pitioss Ruin was fantastic. And it was so nice to drive around, hunt, camp and sidequest in Lucis and find the optional dungeons and tombs.
~Battle System - I hate hate hate hate hated XIII's. I spent literally the entire game just picking "auto attack" from the menu and paradigm changing. While yeah, the paradigm switching stuff was a cool idea that was the most gameplay the fights had. I just used auto-attack because it picked the best options anyway, I never had to go in and decide what to use. The levelling was also super boring and just straight progression except you had to go into the menu to pick the things. Now, the combat in this isn't great and many could argue "all you do is hold O" which, yeah, I guess, but I personally enjoyed it more as it was more active with positioning, magic/item/tech use, warp striking, weapon changing etc. Plus the XV AP point and ascension thing is a lot better than the Chystarium.
XIII Better:
~ Story telling - While the story might not be great it was at least told better than XV. I remember bits being contradictory (stuff like fighting their focus by literally doing exactly their focus) but it was better presented, more cutscenes, better shot cutscenes, more time spent telling a story and expanding on the characters. The characters on the whole weren't likable and quite annoying but at least time was spent on more of them compared to XV. Even if some villains like librarian and guy that looks like Zexion from KH were given as much shaft as most FFXV characters.
Same:
~ Music - Both have fantastic soundtracks. The edge maybe goes to XV but I dunno.
Ubisoft could learn something with SE
Pitioss (the secret dungeon) has better layout and jumping puzzles than most Assassins Creed's
The only (but HUGE) problem is how Noctis controls are terrible for this kind of area.
But I would love to play a game with more of this and good controls
Pitioss Ruin reminded me of Counter Strike climb maps. Intense, long, difficult platforming challenges in game engines not built for it at all.