I'm not sure what a statstic like this would show, when you are comparing airlines with vastly different average airplane sizes. A 747 is a lot bigger than a 737, meaning more seats and passengers, etc., per plane, and you would expect a carrier that has a larger planes in its fleets to have more employees per plane, to handle everything from more reservations to serving more drinks on board. The 737 is the smallest airplane in the UA fleet.
Employees per seat, or better yet per seat mile, may be a more useful comparison.
An excellent point that a lot of folks overlook. The way the numbers worked out for the 3rd quarter:
UA ASM's per employee: 661,500
WN ASM's per employee: 696,400 -- roughly 5% better.
Southwest's productivity is even more remarkable given that their average stage length is under half that of United's -- and they manage slightly higher aircraft utilization even without operating red-eyes or any flights over about 2500 miles. Southwest's yields are actually higher than United's on an unadjusted basis (11.68 cents for WN vs. 11.39 cents for UA), but UA does much better when adjusting for stage length, of course.