Agree with Mike... I don't think they are traditional competitors on paper, but I will say that most people I know shopping in that segment don't have any knowledge of BOF vs. unibody or probably even FWD vs. RWD and just think, "What's the biggest/nicest SUV from: Mercedes, BMW, Lexus, Audi?" etc.
Living in a large metro area that is affluent, the thinking among shoppers is usually: "What's the biggest and nicest SUV they offer?" and then they cross shop 2-3 of them. Naturally, you'll feel a lot of difference between a unibody X7 or GLS and an LX or Escalade, but I can say for certain that at least around here, a lot of people seem to like (and maybe favor) the "big truck" feel of BOF and ability to easily tow more weight.
Looking at MSRPs on dealer lots, most Escalades, X7s and GLSs are $90-100k+ so very much in LX territory, and I think people do cross shop them as such... even more so now with the SUV craze, whereas before the LX had a niche buyer. I think the LX still appeals to that buyer wanting a luxury Land Cruiser that can go 250k miles, BUT I also think more traditional buyers are entering that segment with the "What's the biggest and best?" mentality, and the LX gets roped into the cross shopping more than before.