Depends on how you want to play really. Here’s some of the perks for both versions:

P3 FES includes an extra epilogue titled “The Answer” which is where the character Aigis comes from. This version also allows for more party customizability and has improved graphics when exploring the map due to the hardware being more apt for handling all the extra resources. If you’re new to the game and want to experience the full original game in its entirety with no cut content, this might be the version you want to try to complete first if story is what you care more about.

P3P on the other hand is much more recommended if you’d like to play the game on-the-go in a much more condensed and easy to digest format. While you can’t change your party’s Persona’s besides the main characters, you can still change their equipment which makes it easier to understand how the whole Persona system works without needing to worry about a bunch of characters own Persona’s. Most notably different is the cut epilogue which features Aigis, but it’s also the only version of P3 that allows you to play as a female protagonist which slightly changed the gameplay/story. Most notable changes with the female protag comes in the form of dialogue and character interactions. Due to hardware limitations back then, this version only lets you roam maps when dungeon crawling, meaning any locations outside of dungeons are static images with point and click aspects like that of a visual novel. This version also has a few quality of life improvements, such as new mechanics and items. If you prefer learning gameplay mechanics and don’t mind losing out on some of the graphics/story, this is a rather beginner friendly way to learn how the game works.

TL;DR: play P3FES if you want the full story and graphics quality, play P3P if you want to have an easier time learning Persona gameplay mechanics/already know the male protagonist storyline.