I read something recently (that I can't find now) about it being better to do cardio before weight training. The idea is that whatever you do second, you're going to be doing when you're more tired, and you want to have the energy to get through your cardio.
Frankly, I've had the opposite experience. I enjoy doing the weight machine circuit and then hopping on the elliptical. The weights wake me up and I'm more raring to go when I get on the elliptical. Also, I feel like doing a half hour of the elliptical gives my muscles a really good stretch and I'm less sore from the weights as a result.
Do you have a preference?