White and Murray are both going to be good-to-great players. Murray obviously didn't get a fair shot to play last season due to injury, and that gave White an opportunity to showcase his skills.
That said, Dejounte definitely seems to be the more vocal and demonstrative player, whereas Derrick seems very content to just try to fit in...and it shows in their play. Guys aren't going to follow a guy without a voice.
They can both succeed in the Spurs system without spiting each other, because they both have very different skillsets and personalities. I don't understand why you want to make this a pissing contest.