It seems that most people who loved XII will dislike XIII and people who disliked XII love XIII. That's because XII is as far different from XII as you can get, complete opposites in fact.

XII was open and encouraged exploration
XIII is a straight line

XII gave you the option to control the AI of your team
XIII does not give you the option to control the AI of your team

XII allowed you to customize your team and level them up freely in any direction
XIII says "this is how your characters are going to progress"

XII only told you what you needed to know about the characters
XIII explores the characters in extreme amount of depth

XII allows you to progress the story at your own pace
XIII progresses the story for you

XII included sidequests for things to do outside of plot
XIII offers nothing until post game

XII was a much larger game with more areas to explore that you could go back to
XIII has fewer places most of which are unavailable once you leave them

XII follows a plot much like VI where a power hungry emporer uses his empire to conquer other empires
XIII ...is a kind of butchered version of X

Comes down to what you prefer. I dislike linearity which is the main issue for me. XIII basically sticks you on a railroad which drives you through the game. No exploration, no customization, no sidequests or minigames. Just get from point A to point B and watch all the pretty cutscenes