The Boundary of Mugen item or whatever it's called, actually does double the stats of a heart marked puppet. It just doesn't show on the stats screen.
I gave the item to my Power Aya and saw proof of the stat boosts. She was able to KO a Defense Yuuka (who is very tanky with physical attacks) in the Human Village Tournament with her 5 hit fighting type while holding the item. Without it, it wouldn't of KO'd it. It also out speeds the puppets that were faster otherwise if my Aya didn't hold the item and can withstand a few more hits unless it's a strong electric or wind type move.
Overall, Power Aya is a very cheap puppet while holding that item that I was able to beat the entire tournament again easily by using her most of the time. And yes you're able to win the prizes again, meaning you can get more than one Boundary of Mugens, but the game doesn't let you in the tournament if you have 2 or more puppets holding the same item.