I've been to all several times, and last December my family and I visited Zion, Bryce and the GC all in one trip.
Trying to think from your POV, my vote is for Zion/Bryce. More opportunities for short day hikes and much more diverse scenery. Plus, I think the drive to get there is more scenic than the GC.
There is a free shuttle from the visitor center up Zion canyon (can't take your car even if you want to) leading to many trail heads. At the end of the road a TH leads to "The Narrows" where you can hike along the stream bed and in the water. Beautiful and very refreshing on a hot day. There are also grottos and overlooks to explore on other trails. See
here. I think you will feel rushed trying to see both parks in 8-12 hours. Personally I would just go for Zion as it's only a couple of hours out of Vegas and there is so much to see there.