There is no good way to do an apples-to-apples comparison, since the flight regimes are so different (most airplanes have a lower speed limit that is higher than the maximum speed of most birds). You cannot do an extrapolated comparison either, since the flight mechanisms of birds cannot really work at the higher speeds of human airplanes.

One somewhat useful comparison is between the energy efficiency of flight muscle tissue versus aircraft engines. That's roughly similar. A quick search shows that birds clock in between 13-23%, while steel-construction piston engines are at about 18% (the most efficient bypass turbofan jet engines approach piston engines in efficiency).

But really, the comparison is quite meaningless, since powerplant efficiency is just one factor in overall efficiency.

The most meaningful comparison I can think of is in low speed, high agility regimes for very small vehicles (interpreting "human" to include all artificial flight, including unmanned micro-UAV).

Here, AFAIK, birds and insects win hands down. Human built tiny rotorcraft are just beginning to even get themselves airborne. For sustained, endurance flying, birds like migrating geese are superstars compared to similar-capability UAVs.