.177 has less stopping power than a .22, what it does have though is more penetrating power, but it does lack the shock factor you get to the rabbits nervous system like you get from a .22, when i say shock factor i mean the amount of shock waves that move away form the area of impact to the rest of the body, these shock waves also have an impact on the kill factor. this means your pellet has to be placed more acuratly on the rabbits head than with a .22, the prime kill zone for both is just behind the eye, but with a .22 you can get away with a misplaced shot to the head, as we all know you should only attempt head shot with air rifles on rabbits.
Its like when the british army changed from 7.62 and went to 5.56, its been found that there is a much reduced shock to the rest of the body compared to the 7.62, in turn this is causing more people to survive been shot from the smaller round than the larger one, and believe me there is a big difference.
I personaly use .22, but my shooting partner uses .177 and that suites him and he makes just as many kills as me, its what suites you at the end of the day. as long as the end result is one dead rabbit, with a single head shot. The rabbit deserves that much at least.
YIS
JS