I seldom hunt with a rifle anymore but here is what I know about scopes and my opinions. A lot of it is going to come down to 1. How far do you foresee shots? and 2. Do you see taking running shots? (the quick draw you mentioned). And 3, how important is light gathering?
A 40mm objective matches most rifles better size wise, in my opinion. They also weigh less. My favorite scope is a 3-9x40 Zeiss and I keep it set most of the time at 6 power. That is a good balance of magnification and field of view. I have a 2-10x50 Leika I got for a smoking price. The optical quality of the scope is unbelievable, but had it not been a Leika and a great price, I would have opted for a scope with a 40mm objective. The 50mm is a bit large for my tastes, but it has a German #4 reticle that I really like. I keep it set at 6 power also for the same reason.
The biggest advantage of a large objective bell is light gathering. So, if you get shots at last light, then it can help you there for sure. Fast target acquisition is more, in my opinion, about keeping the magnification set low enough you can get on the animal quickly. That's why I set my scopes at 6 power.