My HRM syncs up with my treadmill. So they are the same.
Never used Bodybugg, but I go with the Polar HRM. I'm on my third, never let me down! But all these tools have a margin of error -- estimates are estimates.
And what do I care if I lose 1 lb or 0.5 lbs? I'm not going to fuss at the discrepancy between my bathroom scale and my Wii. Just move it on down is all I care. LOL.