If your looking to build muscle and cut a little weight, hit the weights hard. get your cardio in after. It won't take much to exponentially burn fat once your body is heated up. even 15 minutes at the end of your workout. If you want it you will make time! all you need is an hour, primary muscle group, secondary muscle group, 20 minutes cardio. then a quick feed(shake) right after. Your body will carry the the burning of calories for quite some time. If your one of the guys that leans on equipment and face books in the gym get your act together and train for 1 hour hard. It will work if you work it!

workouts will suffer. you are burning up the glucose your muscles need for the intense weight sessions. Taking a 15-20 min break will not allow your glucose reserves to be replenished. You would need to eat a solid meal and first and then a couple hours later you would be better prepared to take on the weights.

EDIT: I should also add if you are trying to cut weight then do you cardio whenever you can fit it in. Certain times are more optimal than others but the main thing is just to get it in. Now if you are trying to build lean mass, then either cut the cardio out completely or just do on non-training days. You definitely don't want to be doing cardio before weights if muscle is your goal.