I agree that accuracy is the number 1 criteria. I successfully use exclusively domed pellets for hunting. Ok, I have killed a few squirrels with Crosman HP out of my Prod but they don't expand at Prod velocity so effectively still a domed. My 177 experience is limited, only 3 squirrels so far, but they were all clean kills with H&N 10.65 grain Baracuda pellets. My Prod has taken 15 mainly with H&N copper plated FTTs, 14.66 grain. They rarely shoot through even with a tune to ~18 fpe but take squirrels cleanly. I've taken 20 with my two 25s. One shoots FX 25.4s at about 930 fps. I've only taken two with it, it seems like a bit much for back yard duty and is pretty long to carry through the woods. The other 18 were taken by H&N FTTs going about 870 fps. All but 3 went through the squirrel and only two ran at all and the furthest they went was about 15 feet.
Good shot placement is necessary to get clean kills but expansion is not. But with 30+ fpe expansion could reduce over penetration and a wider hole should kill more quickly. But I limit shots to those where an exiting pellet will have to go really far to hit anything it could damage. It won't have velocity enough to do damage if it has to go several hundred yards. But still with more powerful guns, expanding pellets to reduce velocity at exit is a reasonable option IMHO.