Butchering quality weakly affects speed (1 turn for every 20 points, minimum 2.5 turns), but it seems to only affect number of results when it’s negative.
game.cpp: game::complete_butcher has the formula.
In short: survival matters a lot, dex a little, str only if it’s below 4 (but then a lot) and butchering quality only if it’s below 0 (but then also rather strongly).