The biggest advantage of camping in Zion is that the shuttle service allows you to walk from camp to the shuttle stop and ride from there. (You can't drive your vehicle into the canyon itself.) As for Bryce, You can generally find a non-reservable spot that time of year as long as you don't arrive on a Friday or Saturday night. There's also Red Canyon NFS CG nearby that is first-come, first-served.
But whether it's campgrounds or boondocking locations, you'll find yourself in some competition on weekends as southern Utah is popular in the fall when it gets a little cold and snowy to camp in the mountains.