A few years ago, we went to moab with a few who have never been there. We were on bikes. We were able to cover so much terrain, so much faster than any jeep could dream of. Take Hells revenge for example, I think that is an all day Jeep trail. It is like a 30 minute motorcycle ride. We rode pretty much every single trail in Moab in like 3 days. Plus a day out at the Sand Wash trails, half a day at Sovereign Single track and a day at 5 Miles of Hell.
My vote goes to bike. You can see a lot more in less time.
We used to go to Moab every April on light-ish dual sport bikes and had a blast but the fun magnified when we started bringing along trials bikes. We'd each bring along one dual sport and one trials bike and mix it up during the week. Dual sports to cover miles, trials bikes to play on the rocks.
If I were going in the summer I'd just take a Jeep and enjoy the air conditioning.