There are 3 focal planes when you use iron sights. The rear sight, front sight and the target. It is impossible for the human eye to focus on any more than one. So the correct method is to focus on the rear sight centering on the front sight, which will a little blurry in comparison to the rear sight but will be much clearer focus than the target object. The further the distance, the greater the chance of missing the target. The main advantage of shooting sights is that you can have faster target acquisition, particularly in dark background situations and very short distances or both.
With optics, you only have to consider one focal plane. The cross-hairs centered on the target and your are good to go. Wait, there is a codicil or two. In dark background situations, you have a greater tendency to lose sight of the target, which is especially amplified with higher magnification. The latter can occur even in better light conditions. Then consider the target is rapidly advancing toward you, the quicker it advances, the greater the probability to lose the cross-hair contact on the vital zone. Nothing to really worry about if it is an ungulate, but what if it is a pissed off bear that is not liking your presence and is determined to do something about it.
What would I recommend? For an all round rifle for all game, dangerous or not, I would use a 2-7 X 30+ scope with a quick detachable or tip-off system.