I will admit that FFXIII almost drove me crazy. Of the series, this was the only one that made me want to throw my controller. Yet, I liked it. This game has its problems, but the good outweights the bad.
First the visuals. The game's strongest point. Every background is gorgeous. From the crystalized lake to the grassy steppe, I just wanted to stop and admire the scenery. This carries over into the battles. The characters do far more than stand in place, rush the enemy, and return. Even repitive battles are more visually interesting.
Second the gameplay. This is the game's weakest point. Players can only control one character in battle, and if that character dies its game over, creating both fridge logic and frustration. The paradigm system is confining and annoying but the AI is surpising intelligent; an improvement over 12's gambits. The inability to change battle team or leader is also annoying and there is no excuse for this. When I realized that there weren't going to be any towns I was disapointed. I don't like dungeon crawlers and especially not linear ones. However, this one struck a cord. Think about it: They have been irrevocably cut off from everything they know and love. Of course they're going to be isolated. The 'keep moving' gameplay fits with the story; they can't stop or they'll be killed. I actually found the game hard to put down for this reason.
Second the story and characters. First of all the datalog is NOT neccesary to understand the plot. You can go the whole game without reading it, though it does flesh out non-essential details like the function of non-boss Fal'cie. The storyline, while different from previous titles, is not bad. In Media Res allows the story to develop from both ends; the flashbacks of what happened pre-game influence how the player sees current events, which continue moving. The final parts of the game can be confusing because the game doesn't spell everything out but players will understand if they pay attention. The interaction between characters is gold. I felt for them in their despair and lack of purpose. The ways they deal with being L'cie and find out about the 13 days is well told and interesting, though it DOES take more linear dungeon crawling than I liked.
Bottom line: I like this game. It has flaws, but they're mostly in the battle system.