Thinking about it more, maybe the better approach is the 2nd team works on the oldest tickets. That's an objective measure that has no surprises and more directly addresses the problem of long-standing issues that are sometimes embarrassing because they turned out to be easy.

But in general, I do believe that teams should be split on the priority issue in some way. If all you are doing is chasing the highest priority stuff, you're going to miss important things because priority isn't an exact science either.