I decided to write this review to counter the one that said "it isn't as good as Persona 5".
That might be true (yet to play Persona 5 due to not opening a PS4) but it is sort of like saying "Back to the Future 1 is terrible because it isn't as good as Back to the Future 2" or "Godfather part 1 is terrible as Godfather part 2 is superior". You could technically say those statements but it is dismissing all the work that the previous entry put into establishing the universe and system.
Prior to playing Persona 4, I couldn't envisage how any game could top the story and characters of Persona 3. The overall system was a lot of fun, the characters and interactions memorable and the conclusion was brilliant. After playing Persona 4 though, I struggle to go back to Persona 3 as so many quality of life improvements were implemented in the 4 that makes 3 seem clunky by comparison. Somehow they also wrote even more engaging characters (Yusuke is more relatable than Junpei, Yukiko is more real than Mitsuru, Chie is more fun than Akihiko, Rise is less annoying and more helpful than Fuka, Margaret is way better than Elizabeth), a better location (spent a couple of years in rural Japan and Inaba is spot on for how these towns look and feel), and the gameplay was even better.
The main downside for the game is that once the mechanics are understood (which is not difficult, the game holds your hand quite a bit) it becomes relatively easy. A few battles are still complex but mostly you want the shadow world sections to finish so you can get back to the story. Spend a bit of time at the beginning grinding extra levels and the game is very easy as you are almost always ahead of the difficulty curve.
I can imagine that with everything that is great about Persona 4 is made even better in Persona 5 and the few problems are fixed up making Persona 5 seem like the better game. That is the nature of game development. But if you have played 5 and want more of the series, go back and play 3 and 4 but judge them on their own merits and enjoy the story and the people you meet along the way.