People's opinions seem to differ greatly on this. Personally I liked XIII-2 more, but it does have some issues.
XIII is balanced a bit better (meaning overall the game is tougher and requires more strategy) but it has some obnoxious quirks like if the lead character dies, it's instant game over (this SUUUUUUUCKS I'm sorry it just does wtf were they thinking; XII didn't screw up like that). However, the optional side-quests that let you fight things in XIII are fun. XIII also starts INCREDIBLY slowly. It takes a VERY long time to open up, and a lot of people burn out on it.
XIII-2 has fucking QTEs, but they aren't terrible imo. It also has some puzzles which people seem to hate, but I didn't mind and also the internet exists if you really can't stand them. People also disliked that parts of XIII-2 were paid DLC when it first came out, and that's a VERY valid complaint, it was a terrible choice, but it's no longer an issue.
XIII is a bit more melodramatic/serious and has a better focus on multiple characters- it's more about character drama than plot really-, but the script is... sometimes it's really, REALLY bad, and I thought XIII-2's was a bit better. 2 also had a more interesting antagonist, I think, but the game often takes itself less seriously than XIII, which some people don't like. I'm ngl, I did not like XIII's story, so XIII-2's deviations didn't bother me like they did bother many fans of the original. In the first game I wanted to strangle most of the cast members for most of the story, lol. YMMV. Hard to say whether or not you'll jive with it, some people love one or hate the other, some hate both, some like both.
There are NPCs you can actually talk to in XIII-2, which is nice, but it also means that XIII is a more unusual JRPG because most of the time it's just the party talking amongst themselves or facing off against enemies. The XIII games have data logs which flesh out the story; it's not that you won't get it at all if you don't read them, but you might be confused at first because unlike other games, they often don't have the characters use exposition for the audience (although they constantly remind you that they are
"SPOILERS OF COCOON!"
for some reason, lol) and they use some technobabble (I'll try and fix that for you at the end of this post).
Personally, if you've tried to play FFXIII and didn't enjoy it, I would consider watching it sped up on Youtube and then playing the sequel. But if you haven't played it at all, I would at least try to play the first one, or maybe watch a little bit of gameplay to decide if you want to try it out? Here?:
https://www.youtube.com/watch?v=8s4cUWCixA8
Oddly, the third game is my least favorite, though it probably has the best combat of the three. I could not get over how atrocious the story is in 3 is and I didn't care much for any mechanics other than the combat. Most people say the first game doesn't get good until chapter 10.
Chapter 10!
but at least I can think of some sequences I really enjoyed. I did not like 13-3 at all.
For me it's 2 >> 1 >>>>>> 3.
...
One issue people have is the lack of early-game clarity with some terminology. I'll just clear that up for you now without any spoilers:
Cocoon is a location, and you start inside it. It's really big. Sanctum is the name of Cocoon's government. Pulse is another location. It's even bigger. The two places historically have been at odds. If I recall correctly, in order to reach one place or the other, one has to fly (it's been a while since I played these games).
Fal'cie are big creatures that do important tasks. Sometimes they look less like living things and more like structures, but characters will usually point them out to you so don't sweat it. There are Pulse Fal'cie and Cocoon Fal'cie.
L'cie are humans the Fal'cie have made a connection to sort of, there's more to it but I won't go into more detail. Both Pulse and Cocoon Fal'cie can have L'cie.
Eidolons = name of the summons this time around. There are gods in this setting; keep an eye out for when they are mentioned as they become more and more relevant over the course of the games.