'put on the suits' in this case means to get dressed in their ironman and captain america costumes. Boxing matches are in 'rounds' - people box for a set period of time in each round. A number of rounds make up the match. "go a few rounds" doesn't mean to box, but to fight for a while to see who wins. He was suggesting they both put on all their weapons and armour, fight and see who is the better. I think this was from the civil war film? If so, the fight would also resolve who has the right opinion.

“Put on the suites (his Cptn. America’s spandex suit and Tony Stark’s Ironman suit). Let’s go (fight) a few rounds (like rounds of a boxing or sparring match).” In other words, “Let’s fight (to see who is better)!”