I like both equally.
Both shine in numerous aspects to be honest. If you play P3 after P4 you'll notice how polished P4 is, the gameplay and overall dungeon experience is just better. P4 even implemented fast travel which the original P3 and P3 FES lacked.
I think the question of which do you prefer really comes down to which story and characterization you like. The storyline in P3 is rich and deep and it makes you want to learn about what the hell is going on, nothing really makes much sense until later in the game when everything starts to come together gradually. Eventually coming down to a 'save the world, or we're doomed' scenario. P4 revolves around a string of murders, which to me, just wasn't as engrossing. I loved the majority of the characters (except for the moon arcana, fuck that guy) in P3, I got attached to many of them. There are many scenes that are down right touching and on the other hand, there are some hilarious ones too. P4 of course has its moments, but I think the character development is a bit lacking. I find it hard to explain. The story in P3 is driven by the characters, whereas in P4 the murder case sometimes takes away from the character development, not always, though that's probably just me being picky.
Even some of the stylistic choices I didn't enjoy, this is simply my preference of course. For example, P3 is the black sheep of the P3 games in terms of summoning a persona, it is the only persona game to my knowledge in which you shoot yourself to summon a persona, and I just really liked that concept. Then in P4 they went back to crushing tarot cards, stuff like that. Not game changing, it's just the setting and the direction that the game went in. P3 is pretty dark at times, while P4 is fairly vibrant in comparison.
Saying that, P4 rids a lot of the tedium P3 had. You can increase your stats (knowledge, dilligence, etc.) in a variety of ways, your options in P3 were a bit limited. Fast travel, instantly getting the persona compendium at the beginning of the game.
Not trying to put you off from playing Persona 4, just my opinion on the two games. P4 is still great and I've replayed it multiple times.
I can't really think of any tips that isn't stuff you'll figure out, but here's a couple of pointers. On rainy days, you can visit Aiya (the Chinese restaurant) and if you take the beef bowl challenge (3000 Yen) you'll earn a point in three stats, pretty useful, especially if you have no social links to talk to on a rainy day. The book store sells a magazine each month that increases various stats, completely worth it. The Tanaka home shopping channel is on a Sunday (you don't get access to this instantly) though when you get it, it's usually a good thing to pay attention to it. You can get various equipment or items that are usually better than the stuff you'll find from shadows/chests etc.
The first time you play P4 you won't be able to max all the social links, but you can replay the game on a NG+ and you continue with all your stats, money and persona compendium. Of course, this breaks the games flow and balance 'cause you'll probably own an incredibly high level persona that'll destroy the first couple of shadow bosses, but this allows you to go straight to the social links you missed and some other secrets. Persona 4 has a lot of stuff you'll miss out on the first time, it's probably best to look at various online guides after you finished to see what stuff you can complete and do.