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Pros:
Wheel clearance that is unchanging. No matter how much the suspension flexes, you will not lose that additional clearance. Does not change driveline angle like a suspension lift. Cheap.
Cons:
Puts more strain on body mounts. Can be a pain in the ass to install if bolts are rusty.
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What he said plus-
1. Less total weight is lifted so the vehicle will not be as top heavy {all things equal}.
2. If you do a one or two inch body lift, it not all that noticable.
3. It will give more room to tuck stuff such as transfer cases and exhaust systems in. Maybe fuel tanks and other stuff, think creatively.
I have 3 inch body lift on my K5 and a 2 inch on a CJ5 that I had and would make use of a body lift on most any 4X4 that I would own. I think the best bet is a body lift in conjuction with fender trimming, a small spring lift and the body lift.
There really is not many drawbacks except that you are limited to 3 inches {1-2 inches if you do not want it to be noticeable}. Yes, you might have to do some fiddling to get everything right but hey,,,,,if you are worried about a bit of fiddling-you might be in the wrong hobby.
Plus, after 20 years of rain, mud, and the elements, the body mounts and the bolts will most likely need replacement anyway. Some of my bolts were so rusted that they were about half the diameter that they were when they were installed.
I have 2.5-3 inch springs {I think}, a body lift and aggresive fender trimming and no inner fenders and I'm almost happy with the way my 39.5 TSL fit. I will add zero rates and a smidge longer shackel to the front which will give me another 1.5 or so.