Actually, in theory that that shouldn't happen TheepicME. If one pokemon has "proud of it's power," It's attack IVs are going to be one of the Following:0, 5, 10, 15, 20, 25, 30. But if a pokemon has "likes to fight," then that pokemon will have one of the following Attack IVs: 3, 8, 13, 18, 23, 28. So you see that the pokemon cannot have the same attack stat if they are given the same amount of EVs (or Trained Exactly the same). IVs are a confusing concept to grasp, but once you understand them, they seem so simple. For more information on characteristics, I find that bulbapedia helps a LOT.
Check out this link for more Characteristic Info: