FFXIII is worse than X in almost every aspect. From the; story, characters, to the minigames and level design. I can't comment much on the battle systems other than its just.. different (I liked the fluidity of the paradigm system in FFXIII).
Both games are indeed quite linear. FFX has towns for you to rest up in and allows you to other things, should you wish to take a break from progression. Something which is not possible in FFXIII. Also, with the latter being a lot more linear until you reach a certain point in the game - though this personally didn't affect on my enjoyment of 13. Adding to that, customisation in X with the sphere grid was so much more comprehensive and expansive in the way you could build your characters than what you given with 13.
With that said I enjoyed both games, despite their quirks. I just liked FFX more. For me, FFX is the better game, though it still pales in comparison to the older titles, in the pre-Squeenix era.
