If you make a perfect brain shot, or a perfect under the wing pit on pigeon shot, then what pellet is irrelevant at normal ranges. No pellet shape will make any difference to the outcome of poor shot placement. A .177 is marketably easier to get perfect shot placement due to its higher velocity over a .22. A .22 certainly sounds to give more wallop but if it doesn't hit the mark it won't do the job.

So, use the most accurate and consistent pellet in your rifle, and make that one good shot of it.

It really is as simple as that.
Anything more is the fun of testing, just like testing the rest of your kit. Its part of the fun of the hobby and the results are fun too. The more confident and familiar with your kit the better you will be.