The problem is not really power. I have a powered "exoskeleton" - AKA Piper Cherokee - that allows me to fly perfectly well. And I could use another sort of exoskeleton - a hang glider - to fly in much the same way that large soaring birds do.
No, the real problem is flapping flight, at any scale or power level. To do that reasonably well, you need a highly variable and controllable wing. Birds don't fly just by flapping a stiff wing up and down. The shape and angle are continuously changing so as to maximize lift & thrust on the downstroke while minimizing air resistance on the upstroke https://en.wikipedia.org/wiki/Bird_flight They do this with multiple joints and actuators (bones & muscles), feathers that are controllable with muscles, or which rotate in their sockets, and a complex feedback and control network (nerves & brain).
So to build a bird-like flying device, you have to duplicate all this, and make it reliable (or at least fail-safe). Once you've done that, applying sufficient power should be relatively simple.
Another problem with having humans fly with powered exoskeletons is that our arms are in the wrong place. They're too far forward, so we'd be tail-heavy and crash unless the exoskeleton could flap with sufficient power & speed to hover like a hummingbird. And having our arms forced to move that fast (and probably at unnatural angles) might do considerable damage.