You should be doing both. Doing a lot of solid state cardio (i.e. treadmill) will lead to some loss of muscle mass, so you need to counteract that with strength training. The most optimal way to burn bodyfat is with HIIT training; plyometrics, power-based cardio, the kind you see on the P90X and Insanity programs. I like to combine these two things when I train. So, for example, I'll do a set of squats using heavy weights (heavy for me), and then immediately follow up with something like box jumps, or squat jumps, lunge jumps, etc. I don't always tie the HIIT exercise to the same muscle group as my strength exercise . . . So, I could do something like deadlift, and then 60 seconds of high-knees, or something like that. Those aren't really the same muscle groups directly, but I think the point is to challenge your heart-rate, while also building muscle. I've found this to be very effective for me, having gone from 248lbs to 154lbs in under 2 years, and from 38% body fat to 16% body fat in the same time. If you want, check out my training log, should what I wrote above not make sense.
HIT Rob knows a ton about this stuff. You could look into his training as well, and ask him a question.
My Training Blog: http://veganbodybuilding.com/forum/viewtopic.php?f=24&t=35725