most trainers agree that it depends on what your goals are. If you are looking to lose weight, diet is far more important than the gym (although going to the gym is good for everyone) For me i do mostly weights because I hate the cardio machines but i still do about 20 minutes on one of them just for the obvious benefits of increasing your heart rate. However, i can get my heart rate up just fine by going with lighter weights with higher reps and no (or short) breaks between sets.

It can just be a bit difficult to pull this off in a crowded gym because circuit training is kind of a jerk move if there are lots of people around.