Along with pressure differences, don't forget to allow for the internal construction of the regulator itself. Everything in the breating path is based on balance-of-forces. While we usually think of the forces as water-pressure and gas-supply-pressure, there's also a gravity, and probably a few springs in there as well (depending on the exact details of the reg's internal construction).
If you assume a basic piston-in-a-sleeve type valve arrangement, it's entirely possible that when the reg is in your mouth and you're looking down gravity tends to open the valve (this is also the same orientation for the reg as when it free-flows mouthpiece-up). When you're looking forwards, the piston rides against the edge of the sleeve, so the weight of the piston doesn't affect breathing-work (ignoring piston-sleeve friction). However, when you're face-up, the weight of the piston tends to close the valve.
Even for a 1-gram piston (about 1/30th of an ounce) the difference between face-up and face-down is going to work out to about the same amount of suction (i.e. breathing effort) as it takes to drink through an 8cm (3.5") straw.
Of course, I don't have schematics for a reg handy, so this is all just theory.
As for the "Air wants to go up" statement a few posts ago, Ummm, no, it doesn't... Air wants to go down, as does everything else in earth's gravitational field. It's just that the water wants to go down more. But when the reg's in your mouth, the gas in the reg is only compared to the gas in your mouth/lungs in terms of bouyancy, and there shouldn't be any signficant difference.
Jamie