I don't see either UCLA or USC leaving for the new NFL stadium. USC will begin a major renovation of the Coliseum in a year. Additionally, the Coliseum is adjacent to the University. The last thing USC wants is to be like UCLA - busing your students to a distant stadium.
The Rose Bowl has a great history and is a beautiful stadium...the parking situation is indeed poor as many have mentioned here. I can't see UCLA wanting to give up this stadium either.
I do not expect USC to move to the new stadium because their long history with the Coliseum and proximity. It makes more sense for UCLA since they do not have a long tradition with the Rose bowl and the distance is similar. The Rose bowl may be a beautiful venue site but it's 1922 design is functionally obsolete. There is a reason the NFL passed on both the Coliseum and Rose Bowl as potential demos and rebuilds. They are looking to improve the game day experience and neither of these sites qualified for what they wanted to build for many different reasons.