I don't think it's possible to say which is more accurate. You just have to find a known accurate gauge to compare them against (or at least compare one of them against a known accurate gauge, then compare that one against your other one).
If your handheld gauge is Schraeder valve, you should be able to find an ISO-certified auto or truck facility with an accurate tire gauge to calibrate yours against. Be sure it's ISO-certified though. Lots of auto dealers and tire shops don't bother to calibrate their gauges at all.
Tire service people at motorcycle races (international events excepted) are usually happy to calibrate a tire gauge, when they're not busy with the race tires. Probably would be the same with auto club races. I'm not sure how tire service works at major bici events, anyone?
Speed comes from what you put behind you. - Judi Ketteler