SLIGHTLY different perspective from Wayfarer:
I think that the GX is probably pretty capable offroad...for what most people would want or need. As long as an SUV has a 2-speed transfer case and a locking center differential, it will go most places. So, I'd say they're both capable, but certainly the LR3 has an edge because it is designed for even more extreme stuff and has greater technology (traction control, suspension, locking rear diff (if equipped with HD package) and of course the TR system). ...but for most people this is over-****.
Which brings us to other criteria: The GX is probably more reliable than the LR3. There, I said it. I haven't had any issues for a while (knock on wood) but when I was having issues, I was very unhappy. The GX is a Lexus and it's in its 4th (?) year of production so it is most likely quite reliable. It's also sort of conservative and boring. That was my take on it when I drove it.
So there you have it.
They're both nice and you really can't lose either way.