Right, I have both an Armada and an LR3. The Armada is a pig. A very fast pig, but a pig nonetheless. It has a FANTASTIC engine, but I get 11mpg no matter what. I got 16 mpg coasting down out of the Rocky Mtns once....only once.
The Armada is huge. It fits everything and anything and everybody all at the same time. I am 6'-7", I fit comfortably without modification. I had to modify my LR3 to fit me better (extended the seat rails 3"). The power liftgate is really nice. I teased my wife about it a lot, but now I want one too
The cargo space is volumnous. Sheets of plywood fit. it's amazing.
The Armada's ride is crap compared to the LR3. The LR3 is so much more nimble, poised, smooth, and refined.
The Armada has very little off road capability. The traction control does work fairly well, but it's street oriented and quickly overcome by rocks and things. The LR3 is superlative off road. Widely regarded as the best off road vehicle ever made by Land Rover, and that is saying something.
If your family will fit, they will love the LR3 more. If you need the space, the Armada is the ticket.
In my family, we did a "one lap of america" tour last year in the Armada, because we fit so well. We even took it to the National Rally, which KILLED me inside, but I got through it. Right now, I am planning a March trip through Moab, Canyonlands, Valley of the Gods, and Glen Canyon areas via trails only. It will be a vehicle dependent Overland Trip, and ONLY the LR3 will make it. So last week, I modified the passenger seat in the LR3 so my wifes long legs will fit more comfortably (she is 6'-2"). My kids are still small enough that the back seat is okay for them, and now the adults have a bit more room.