Before Vergil awakened Dante's DT ontop of Temen-Ni-Gru, he was stronger. So all you have just said is that you have only considered things in the game, and not what is stated outside of the game. Both twins are equal in strength. Vergil is a BOSS in the game, and you HAVE to win as Dante to advance. Just because you have to win, and do, does not mean he is weaker than Dante. Play the fight, and you can die a couple of times. It is an equal match, nuff said.
And the only reason he is looked down on is due to how he is shown in the games. Always shown as the weak one trying to get power. Vergil defo beat the hell out of Dante on Temen-Ni-Gru, and he had the perfect chance to actually kill Dante. He didn't take it, and instead he awakened his DT and helped him. Why exactly would he do that? I think that shows a lot of care for his brother. To have been able to kill his enemy, and knowing that he'll probably never get a good chance to do that again. They were rivals because Vergil seeked power, and Dante stopped him because he saw what Vergil was doing as wrong. Vergil's intentions are never truly revealed, Vergil was THE only character to rival Dante, before Arkham and the others came. So in all fairness, he is equal in strength. Not to mention he is a son of Sparda. The same strength lies in his blood, as it does in Dante's. Twins, half demon and half human. Equal.