Well, typically when you are playing a 3v3, he champs thats would be good in 5v5 wont be as efficient in a 3v3 match. Also in 3v3 a crutial part of the game is early game. If you can take the advantage top lane and feed top, then that champ can literally carry your temates to victory.
So, when you play 3v3 try to use champs that not only u know how to use, but are also easy to get fed with. When i play with champs i usually use jax at top, because with his E he can counter any champ in the game, (except for mundo and WW), and he is a hybrid, which means if they build armour then i can just build AP, and vise-versa.
Another Crutial champ to choose is a tank. I dont mean amuamu or Kayle.. I mean champs like Mundo and voli, those are, in my opinion, the 2 best tanks for 3v3.
Heres a good example of a good 3v3 team:
Jax (AD and AP Hybrid)
Voli or Mundo ( exceptionally good in Laning bot )
Shaco, Caitlyn, ect..( any AD Champ That Hits Hard.. Why? Ill explain)
The reason you get an AD champ bot with a tank like voli or mundo is because most tank champs usually are AP, so if the champ builds magic resist then u can still deal damage with cait or shaco. And of course if they build armour then u can get them with someone like voli.
And one more thing.. People like to complain aboit champs like Voli, Mundo, Yi, and any other champ thats "easy to use".. I just want to tell you that no champ is OP, and if it was thrn they would have nerfed them, its how u play your champ that makes them good or not. So if hey complain abput you useing shaco or jax then clearly there not good. Im just using shaco and jax as an example though.
So to sum it all up, 1 hybrid, 1 AD and 1 AP Tank .. Or an AP champ and AD champ.. Whichever u want