Having visited both multiple times, as we have family that lives between both, you have 2 choices, hike or drive. In Zion, unless you hike, there is absolutely nothing to see other than the drive from gate to gate. If you do take the shuttle, it is a couple hours round trip and again, unless you walk a long ways, nothing really scenic that you can't see elsewhere in UT. Bryce offers more for the non walker, but that too can be viewed in a day from the scenic pull outs.
We are going to be spending a week in the Bryce area the middle of August, but will be in the backcountry, not the park. The scenery is much more awesome when you get around the peripheral of the parks.