This is something we have been going back and forth about for a while. We currently have a very nicely setup trailer, complete with awnings and RTT, along with on-board water, electric, etc. It is very convenient to be able to pull that thing anywhere and set it up for camp, especially with the extra storage room that it brings for gear. Thus far, on all the trips we've taken, the most inconvenient part of having the trailer is having to pull it with the fabulous JKU transmission. On mild trails, its honestly not very noticeable (unless you have to turn around as others have mentioned). On rougher trails, especially steeper climbs, you certainly notice that it is there, but it is not necessarily a hindrance, nor has it stopped us from being able to complete a trail as of yet. I like the ability to be able to take it somewhere, set it up, and if we need to run to town or take a side trip we can leave camp set up and not have to break down the entire camp.
Another benefit to me versus having it on the top of the Jeep is, as others have mentioned, with it being on the trailer, I never have to worry about taking it off of the top of the Jeep when its not in use. I haven't ever had it on the roof of the Jeep to compare, but I'm fairly certain the miles per gallon pulling the trailer would be pretty close to the same as having the RTT and gear up on top of the Jeep dragging wind. A final huge thing for us is having the trailer allows us to carry almost all of our camping gear in the trailer, along with firewood, etc. When we go on a trip, typically we have our dog with us in the backseat, and in another few months we'll have a carseat in the back as well. With our current set up, the only gear we carry inside the Jeep is our ARB fridge, food, and any personal items we may need for the road.
I think ultimately, the decision about whether to use a RTT on the vehicle or to pull a trailer really depends on your personal needs. If you have plenty of room in your rig for all your passengers, gear, etc., then having the RTT on the roof would be fine. If you need the ability to haul your cargo elsewhere, then a trailer is the way to go.