Is persona 3 or 4 better?

It doesn't really matter which you buy first.

In the PSP version of Persona 3, you go to the school in Persona 4 during a trip. You even get to see Yukiko, a main character from Persona 4.

In all versions of Persona 4, you go to the school and island from Persona 3. You see a few characters from Persona 3, and you explore the island, mentions a few events from Persona 3, etc.

But in both games, they are so minor, they don't ruin it if you don't get it. Mostly just for fans to go "I know what they talking about".

In terms of better, I'd have to say about equal.

Persona 3 is the darker of the two, what with trying to save the world. You explore the dungeons at night though, which I quite like, as it doesn't interfere at all with the social sim aspect of the game. Also, won't spoil what happens, but the final boss of Persona 3 is memorable and epic, much better than final boss of Persona 4.

Persona 4 is the brighter of the two, as they are trying to learn the truth. You do waste daytime going in the dungeons of the game, but I find this game has a better variety of characters. Only actual bad thing I find is that there is weather, and social links rarely appear on rainy days.

In the end, I'd recommend playing Persona 3 first. You'd understand the little nods in Persona 4, you get to experience the better final boss first, and just for the sake of adding another reason, it was the first of the 2 to be released.

Persona 4 is more lighthearted than Persona 3.

Each are their individual games and they only keep Personas and mechanics, completely separate story.

If you ask around you're going to get mixed opinions. Maybe just see which one looks more appeasing at first glance because they're both pretty good.