Often a recording kit will be setup for less resonance than a live kit. This is why many drum recordings use a birch kit, which has a sharper attack and less sustain, while live drummers lean more towards maple, which has more sustain. Live, you really need a some sustain for the drum tones to be heard. If you close mic each drum on your kit live, this is not really an issue. But if you play live with minimal or no micing, the extra warmth and sustain from resonant heads on a maple kit goes a long way.
Carter Beaufort from Dave Mathews mics a birch kit for both recording and live use, and you can hear this in his very distinctive, tight sound.
If you want to muffle your heads without killing the sound, you can try Moon Gel. These are little sticky gummy bear type things that you put on your heads. You can precisely tailor the amount of muffle and ring you get by placing them closer or farther from the rim. They give a much better sound than any other muffling I've tried.