I heard you should do whichever activity you are most concerned with first. For example, if you are really focused on building strength, you should do your weight workout first since you will have the most energy for that. Conversely, if you are more focused on cardio, you should do that first and save less energy for weights afterward. However, I have also heard some of the arguments posted above. I think there is a bit of controversy on this issue in the fitness field.