I should be gone by now, but I wanna finish my new FF15 themed avi before I bail.
Hope for spoilers to not get me :S
The main difference between the two is in its excussion of "why" you are in a straight line and the world building.
XIII tried to signify to signify the idea that the characters have nowhere but forward to go, but failed to account for how the world mattered to that end. Nothing gelled together into a cohesive whole for its world.
X on the otherhand is all about a Pilgrimage and the slight sidesteps along it. It is entirely about the journey, key to the story and to the world.
That last point about the world is key. XIII's inability to show us the world beyond the "we must go forward" and the almost entire focus on Fal'ce is completely opposite to X where things are about knowing the world as you go and more importantly why Sin is such a big deal to begin with. X gives you a reason to go after the god-like being, not through force, but by showing you a reason, XIII does the exact opposite. Which is exactly why things like zenophobia and religion as themes in X work so well and work so poorly in XIII.
XIII really fell flat because of its story imo, not its linearity