A lot of different opinions here. Mine is also apparently very different too.
I loved FFX, I think it was the best story line of the modern FF games, and as others have said, while it was apparently linear, it often didn't feel as such because there where many towns and villages where you could wander round and chat to people doing side quest. It was the last of the old battle system and worked very well. I would have been happy if they decided to continue with this system. While slow, it's the most tactical of battle systems, while slower, I found it more engaging.
FXII was a good game but I liked it distinctly less, The battle system with a good gambit system left me wandering over to a group of enemies, and then wandering of to make a cup of tea while the characters won the fight themselves. I enjoyed customizing the gambits to be as efficient as possible, but the fights themselves where comparatively a let down compared to FFX. I also found the story a bit boring and predictable, my main hang up was the lack of character development. I got to the end of the game still wondering the point of including some of the characters, they where more assistant fighters than characters. The two Pirates and Princess Ashe (sp?) where very good characters IMO, unfortunately this was off-set by the other 4 boring characters, including the main character who I didn't particularly like. This is of course a problem for a role playing game, if you don't particularly person you are supposedly in the role off. Normally you play as a leading character in FF and perhaps they should have stuck to that, or at least make the player you are playing have something about them rather than being someone along for the ride. Penelo (sp?) was so anonymous, that I can't even remember anything about her other than she is friends with Vaan. It's such a shame that I feel the characters and story let the game down because the world was excellent, and was possibly the best of the modern FF's. There was no shortage of cool locals, and it was expansive, allowing you to roam free.
FFXIII is a very good game in my opinion, the story's decent, although the plot line is perhaps not particularly special, playing through the game is particularly fun, the locations are pretty cool too. The characters are very well developed, I could tell you plenty about each character. I liked most of them, especially including the main character (although main character is less obvious in this game) Lightening, who is certainly an intriguing personality (with a very cool weapon). The battle system is far more involving than FXII and relatively tactical, on top of that, its quick flowing. I wouldn't say it's better or worse than the FFX system, its just different and perhaps for many, that was necessary. The main problem with this game is the linearity, the inability to wander round and chat to people and take on side quests turns it into an A - B chase the objective at all times. This only stops being the case at chapter 11, which is many hours and percent into the game, and even then there aren't particularly many side-quests beside a very comprehensive 'monster hunt' style side game. While this is very good, it's not enough stop FXIII being linear. Another negative factor is the levelling system whereby all the characters get CP, so a character you never even uses can be just as good as the others at the end of the game, for me it defeats the point of specializing roles and training a character into a specific role, it makes things too easy in my eyes. The cyrstelarium is also very limiting and linear, its no where near as good as sphere grid from FFX, which basically allowed you to fashion your character into whatever role you wanted them to have, it took planning and was vast, a much better approach. I don't see how giving you less choice is a good thing for a game like FF, simplifying things makes life easier but at the cost of enjoyment IMO. Thankfully they decided to make the weapon system more involved and for me the weapon and experience system is very well executed.
I enjoyed FFX the most out of the Modern FF's followed by FFXIII and then FXII.
Of course, each to their own.