Hi Mate,
I've always shot with a .22 and whilst you do get the occasional incident where you don't get a direct kill, I would say it happens very rarely. Usually when it does happen there will be a simple explanation (e.g. pellet hitting a twig before the target, blustery wind, target getting spooked at the very instant you pull the trigger) but I can't think of a single incident where I've hit my intended quarry cleanly and not killed it (and I've killed a few hundred rabbits and a few hundred more pigeons!)
However, I can't imagine that a .177 would be any worse at killing than a .22. T