Stayed two nights at each in 2005 when my kids were 14 and 12. Knowing what I know now, if I only had two nights, I would just stay at Bryce and skip Zion. However, my wife says she would two nights at Zion and skip Bryce. To help you decide, I'll share what we did and enjoyed at both.
At Bryce upon our arrival, we had enough time to drive the road to Rainbow Point and get oriented from the overlooks. Next day we drove around to Mossy Cave Trail in the morning and then did a short hike down into the Hoo-Doos from the top. We also signed up for a half day horse back ride down into the Hoo-Doos. Last morning there, we moved the FW to a parking lot near the corral. Then the kids and I took the trail ride while my wife relaxed. After a quick lunch we moved down to Zion.
At Zion, after setting up camp in South campground (no hookups), we took the shuttle up to the end and did the Riverside Walk along with a few other stops on the way back down. Next morning, the girls and I took the bikes via shuttle up to the end. Since the shuttle only carries two, I took the first shuttle and let the girls ride on the second shuttle together. The ride back down is mostly gentle down hill with only one very short steep hill and the last 1/2 mile flat along the river. Was very neat being able to stop along the way where the shuttles don't. The shuttles are always on the lookout for pedestrians and bicyclist so no worries there.
Regardless of which way you do it, you will be glad you did.