The storylines for both were fairly equally ludicrous. I probably prefer XIII-2's story slightly better because it had time travel, even if the time travel didn't make a ton of sense and didn't seem to matter in the end.
As for characters, X-2 had Yuna and Rikku who for some reason were much more annoying versions of their X characters, whom I liked. However, it did have Paine, who was pretty cool. XIII-2 had Serah who was more annoying than anyone in X-2 but it also had Noel who I thought was a very good character (great character even). So XIII-2 wins by an edge here.
Gameplay, X-2 wins hands down. It has the best ATB of the entire FF series. Chaining attacks and having job changes mid-battle were great additions. Put a version of this in FFXIII and it's a much better game. Unfortunately, the XIII series evolved the ATB in all the wrong directions. XIII-2 did a great job fixing some of the most glaring problems from XIII that never should have been there in the first place (game over when leader dies? Come on, SE) but it was still that inferior paradigm system with the uninspiring crystarium.
Overall I give the edge to X-2 even though XIII-2 is slightly better in the non-gameplay elements. X-2 was just overall more fun.