I really wonder how many of those people who "universally hated" XIII-2 actually played it. I really disliked XIII but I absolutely adored XIII-2. Fixed pretty much all the problems I had with XIII.
As for X, my least favourite Final Fantasy. Cliched story with twists I saw coming from half a mile away; linear as hell (seriously, this was the Final Fantasy which started "corridor syndrome"); most of the cast is absolutely terrible (Lulu and Auron save it from total disaster). Soundtrack is good and battle system is decent, though.
I have been convinced by a number of people (Brendude & Padib most prominently) to give it another chance, though, so I'll be buying the HD Collection when it releases so see if it's as bad as I remember it.
I actually really loved FF XIII-2. It's one of my favourite Final Fantasies. I really wanted to throw my copy of FFXIII out the window :/.
I don't think you'll enjoy FF X. The cast is indeed very well done, but if you don't like them, not much is gonna change you on it. Combat's still the most strategic in the series; it's a shame they made it too easy to utlize.