I get this question a lot. I also have witnessed people doing their cardiovascular routine before they lift weights when working out. So which is it?
My view and application to exercise changes with each client and over time. Back in the day I was so set against cardio before lifting weights. Now, I have gone against that method from time to time. However, if you are looking to build strength, cardio should be done after you lift. Why? First, you need max blood flow and energy to get the most out of your lifts. There's no need to have the muscles fatigued, depleted of energy and oxygen from cardio when you are trying to go to muscle failure for strength goals. Second, injury prevention. If you are fatigued from running before you hit the weight room, you might be setting yourself up for injury.
If I see a client two times a week and their goal is weight loss, then I will try to max out calorie burn as best as I can by burning the candle at both ends. I love to circuit train those type of clients by having them perform a weight set, followed by cardio for about 5-7 minutes, and then back to a weight set. Any combination will work, plus, time moves a little quicker for the client if they are always engaged in something. It's great for the heart too! Here's a great example: