I had a chance to play through FFXIII-2 finally.
TL;DR: Overall, it's a good game. The story struggles in places, however. But if you liked FF13, you can't pass this up.
As far as the mechanics go, you can tell they put a lot of effort in including the things that 13 lacked. There's less linearity, there's mini-games, and there's people you can stop to talk to. Contributing to the freedom of exploration is the addition of both time-traveling and even travel to parallel universes. But more on that later.
The game still relies on 13's iconic Paradigm Shift battle system where the focus is on shifting your team's jobs at strategic moments during combat. A new addition to this is the Tune option where you can configure your battle line-up to focus on a single target, multiple foes, or use their default judgement.
I felt the pacing of combat itself could have used some fine tuning. The bulk of random encounters are battles that are over too quick with little strategic consideration (sometimes you can literally do nothing while your companions auto-kill all your opponents and still get a perfect 5-star rating). I think this leaves you ill-prepared for some particularly brutal fights you occasionally get yourself into along the way, where having a good grasp of using Paradigm Shift teams is essential. If most fights are over before a Saboteur can land a single debuff or before you'll be hurt enough to even consider a Shell from a Synergist useful, you probably aren't going to see the value in these jobs until it's too late. That aside, the big fights are very engaging, and if you get lulled by the seemingly easy-mode encounters up until you hit them, you will get "pantsed."
The real weakness in FFXIII-2, however, is the story. What really irked me the most was when the obvious shortcuts turned up. Right in the beginning, for example, the story requires Noel to do something heroic for NORA so that they'll trust him enough to whisk Serah away on their little adventure to save all of existence. So they do this by having him carry NORA-girl Lebreau, who was injured in a battle he participated in, back to her house. But rather than have him carry her directly to a bed inside the house (the beds you see inside the house when you first start playing as Serah), Noel dumps her behind the staircase in front of her house, saying she just needs to sleep off her injuries and she'll be fine. And then he and Serah have a pleasant conversation as though leaving her injured companion lying on the ground unconscious outside their house was perfectly normal. Gah!
But it's more than just that. There seems to be a ludicrous amount of bizarre explanations used to have supporting characters re-appear in different time periods centuries apart (not having aged a day) to mask the fact they obviously didn't want to make any more characters. The result is more fish tale than epic adventure, ruining what could have easily been a great story with just a little more effort. One only needs to glance at Square's notoriously good time/dimensional traveling Chrono series to see how a proper RPG of this caliber should be made.
And it's really sad, because the beginning and ending (especially) are riveting, unique, daring. How the game ends should upset you for all the right reasons, and I like that it challenges me that way. I just wish I could have been as drawn in for the generous middle of the story instead of grappling with my disbelief.
That said, the game does pretty well overall. The mechanics are sound, you have a lot of freedom to explore, build up monsters for your team, play games, collect treasures to enhance your party, and even take in a few alternate endings or challenge yourself to some optional "mega-bosses." There's something for almost anyone if you can overlook a somewhat shaky story.