Persona 4 is considered a anime fighter which play a certain way. KOF 13 is a bit more of a traditional fighter. KOF is really offensive and fast paced, but it is harder to play and the online is bad. So if you have the time and some friends to play with I would suggest picking up KOF.
On the other hand persona is way more simple to pick up and play. However the game does have a deeper element. Also the online component of the game is much better than KOF. Me personally, I much prefer KOF. I feel it allows for more fighting game fundamentals. I also enjoy how fast paced it is.