I think I burned through the batteries that came with the wiimotes within 12-16 hours. Duracell Coppertops lasted roughly 20-24 hours. Currently using Duracell 2400 mAh rechargeables at 15-30 hours between charges.
But yeah, back on topic, of course your GB is going to be consuming more power. Might make the spread further by saying you only have to replace the AA's in your TV/DVD player once a year.