I have to agree with most here that 2 days is not enough to do justice trying to visit both parks. We did just that about a dozen years ago and will have to revisit both to fully explore in the next few years. We visited in July and Bryce was completely over-run at the time. We ended up staying overnite at King Creek USFS campground west of Bryce. At that time, King Creek was a very quiet and nice respite from the Bryce madness. You may want to look into that campground or someone else may want to chime in wIth more current info about King Creek.
Whatever, you decide, both Bryce and Zion are must see National Parks...