While both are old franchises in terms of age, Final Fantasy and Persona both underwent a significant change of direction around 2007 and are currently very different from what they used to be.
My question to you is, do you prefer the modern incarnation of Final Fantasy more, or the modern incarnation of Persona?
Just so we are clear, this is what 'modern Final Fantasy' includes:
Final Fantasy XIII
Final Fantasy XIV
Final Fantasy XIII-2
Final Fantasy XIV: A Realm Reborn
Lightning Returns: Final Fantasy XIII
And this is what 'modern Persona' entails:
Persona 3: FES
Persona 3 Portable
Persona 4 Golden
So, which of these two franchises in their current incarnation do you like more?