Persona 4 has the better story.
Persona 4 takes around 2 hours before you really get any battles, and around 4-5 before you start controlling your everyday stuff and when you go into the shadow world.
The story for VC starts almost immediately
further but unasked for info: Persona 4 is longer (still haven't beaten it at 60 hours) while VC is around 30 hours. Both have very involved and interesting battle systems, but VC has considerably less grinding involved.
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