I think it uses cell tower triangulation and wifi hotspot location instead of GPS for the location-based reminders. I told it to remind me to clean my damn kitchen when I get home...and I got the beep once I got to within a couple miles from my home. That way, it doesn't use much more battery than the phone uses in normal operation. Since it has to connect to cell towers anyway, it's only a slight blip on the radar to ask for the location of those towers when it jumps over to another one.
It's hard to make a repeatable test out of it to determine exactly how much, though, because the power it uses is never exactly the same even in the same route and same usage every day.