So I have to chuckle that the responses the encourage to go with a trailer mounted tent are from guys that sell trailers.
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Just giving you guys a hard time. I have a trailer too so you won't hear me bag on them. But to answer the question, fuel economy is not my primary concern. Of course I don't through all caution to the wind but we all drive heavy offroaders that don't exactly have great fuel economy to begin with so the argument to not use a vehicle mounted tent because of fuel economy is kinda pointless IMO. Just carry an extra fuel can.
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To me the answer comes down to the places you want to get to and how difficult of a time do you want to have getting there. I have a RTT on my truck and another on my trailer so I feel I can speak to both sides. I love having my trailer and if you've already determined you need a trailer to carry the necessary gear then you might as well put the tent on the trailer and not worry about the negative vehicle dynamics that can happen with a tent mounted high on the roof of your vehicle. But if the trailer isn't a necessity there's a strong argument for a vehicle mounted tent. The fact is no matter how rugged you've built (or bought) your offroad trailer it can still be a liability on the trail. It makes everything more difficult just because you have to drag something else through everything you just drove through. Most of the time that's not a big deal, but it can turn into a big deal quickly.
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It really is a difficult question to answer since there are pros and cons to both solutions. I love having the tent on the trailer because I can just set up camp and leave it and go explore and not worry about breaking things down at camp. But on the flip side, it's nice when the whole family isn't coming (which is why we have the trailer) and I can just use the tent on the truck. My mobility is much better and I'm much more confident in the places I can get to without the trailer in tow and I've got my campsite with me the whole time.
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Again I think it is more a questions of do you need the trailer? If you already have the trailer, I'd mount the tent to the trailer, no question. If you don't have a trailer, and are trying to decide if that's the route to go, then that's the bigger question. More often that not, a trailer isn't needed but a lot of people have them for the "cool" factor. That's fine but the definitely limit the places you can go. If you plan to just stick to mild tracks, then load up the trailer and throw a tent on it and go have a blast.