I would want an adjustable objective. I know the side focus is fashionable and convenient to all the multitudes of internet snipers, but the ones I have are coarse and crude, hard to get both focus and parallax correct at the same time. Of course you might get a better scope than my Leupolds.
Air gunners hunting in the field like the side focus (SF) because they're more convenient to use (i.e., only have to move your hand to the side and turn in the range) and your objective lens cover stay fixed in position. If you're hunting from a stand and only take shots less than 100 - 200 meters, you're better off just setting the objective parallax ring (OPR) to a fixed range (e.g., 100 yards) or using a scope without a OPR. I have two SF Hawke scopes for air gunning and I like them and have thought about replacing my Burris and Leupold scopes on my center fire rifles with SF Hawke scopes.