Play the Persona 4 first, see if you like it then go back to Persona 3. If you don't like Persona 4, chances are you won't like Persona 3. They are both very similar games but P3 is less polished.
If you do decide to play Persona 3 first and hate it, give Persona 4 a chance because the gameplay is much more forgiving.
If you can pick what versions to play:
P3 FES > P3P > P3
P4 Golden > P4