I started it recently, but...well, I'm not ready to replay P4 yet after two relatively recent full playthroughs of the PS2 version, so I only have about 10 hours into it and am progressing slowly.
My (relatively shallow) thoughts so far:
Honestly, it was the first game that really showed me the graphical capabilities of the Vita. That is, it's bright and much smoother than I was expecting after P3P. I can't wait to see how the handheld looks when it's pushed.
I don't like the new battle theme, but fortunately Reach Out to the Truth plays when you get a surprise attack.
I adore the costume changing at will. I wish they had this in the original.
Marie is absolutely, utterly obnoxious and I can't stand her.
A very nice touch was the addition of new NPCs running around in background scenes. For example, when you're walking to school you'll often see your schoolmate S.Links (think Naoki, Ai) running by, while the generic NPCs talk or your friends chat with you like they did in the original.
The new Shuffle Time is really easily broken in just about every possible way. However, it also lets you use older Personas that you would have discarded. You can make a godly (no pun intended) Izanagi if you'd like, with a little time and effort.
And, most important of all:
Thank you, thank you, thank you for letting me choose inheritable skills. Now I won't have to shuffle for an hour to get my invincible Helel.