When breeding in all versions of the game, IVs are generated randomly from the IVs of the parents. Any items given to the breeding parents influence what IVs the offspring will have, however, it is still random.
|| Example as follows ||
Special Attack: 31
Special Defense: 31
Special Attack: 0
Special Defense: 25
If you were to breed these Pokemon together, and lets say you gave one of them a destiny knot, you would have an offspring that would have 5 guarenteed IVs from the parents. That doesn't specify which IVs will be passed down, just that 5 IVs total plus one random will be passed down.
The way the power items work (I'm pretty sure anyways) is that instead of guaranteeing that 5 IVs will be passed down (like with the destiny knot) it instead guarentees the one IV that the power item is designed for. I've never tested it with both parents having the same item but I imagine the effect would be the same as you cant guarentee the same thing twice.