If Your Goal is Increasing Muscle Size and Strength
Increasing muscle size can best be accomplished by lifting weights first when the body's main source of energy for muscle contraction (glycogen) is high. If you do a hard cardio workout before lifting, you deplete glycogen, which makes the workout ineffective.
After.
Everyone's goal here should to be getting stronger. Strength increases endurance (whether its running or pullups or whatever). If you want to lose weight, strength makes you strong AND makes you lose weight.
People in general, especially here, should be focusing on strength. Even emergency personnel who should be focusing on metabolic conditioning should have ample strength components to their workouts...in which case strength should still come first.
If your muscles are not fresh then neuromuscular efficiency goes down and it is much harder to get strong. If you are going to waste your time doing endurance activities before strength activities then you are better off not doing a strength workout at all for that day, imho.
EDIT - if you read that article in more detail it pretty much always says to put endurance on its own day all together. If you are going to do it on the same day and your goal is endurance then you are missing something. Also, you should probably read this so that the concept of doing endurance work makes more sense:
http://eshlow.blogspot.com/2009/06/why-speed-work-is-necessary-for-elite.htmlI can't honestly think of one valid reason people should do endurance work before strength work.