For a serious answer, I would suggest playing Persona 3 first, over 4. This is mostly due to a personal bias, 3 is my personal favorite, and I think 4's story and characters are extremely messy, to say the least.
Persona 3 however has two different versions of note. Persona 3 FES, originally for PS2, is an updated version of the original P3, also on PS2, which makes playing the actual original pointless. I will get back to this version in a moment. The other version of note is Persona 3 Portable, which was made for the PSP, this version actually has a significant number of differences from FES, so it's worth going over.
The biggest difference between Persona 3 FES and Portable is in terms of presentation. While FES will present the game in a similar enough manner to how you'd be used to from P5, and potentially P4, Portable instead shifts the presentation of cutscenes to a visual novel format, and all exploration outside of the dungeon is done through something more resembling a point and click game. In my opinion, this change in Portable is enough to severely hamper the experience for people playing P3 for the first time.
A common point I see brought up when suggesting Portable over FES is the subject of party control. Yes, FES does not allow you to directly control your party members, only the protagonist. Everyone else is controlled by the A.I., while Portable lets you control everyone directly like every other game in the series. While I understand the frustration this can cause, I would argue there is not necessarily a problem with it, as in practice it's not that hard to plan around this, using tactics, or attempt to manipulate the A.I. into doing certain things. More importantly is that the game is sort of balanced around this fact to begin with, but Portable gave you this, and other abilities, without actually trying to rebalance the game, making Portable really easy and simple to break.
On the subject of actual exclusives, the two versions do have some unique stuff. Most notably is FES's epilogue chapter, and Portable's new protagonist.
FES adds a new playable chapter that takes place after the end of the original game, called "The Answer". This part is often criticized for it's writing, and while I disagree on some common complaints, I think I agree with most people when I say the gameplay is terrible. The Answer is just a non-stop dungeon grind, with the game fixed on the highest difficulty. It's a chore, but thankfully is easily ignored, since it's optional.
Also optional and easily ignored is Portable letting you choose to play a male or female protagonist. There's actually quite a few differences between the two. Still, if you play Portable, I would recommend the Male protagonist route first, not just because he's the canon and original playable character, but the female protagonist is... weird. I won't go too into depth because... read above, do I need to keep talking at this point? Anyway, point is the female protagonist is kind of odd, as her demeanor sort of clashes with the games intended message and arc, and while the female protagonist has several different Social Links than the male protagonist, most of them are very poor in comparison.
Of course, this is all opinion, but it's always worth hearing different sides.
Implying you didn't just skip that wall of text.