Good topic... I like it but it's difficult to make a one situation fit's all decision.
Here's a chart of the data for the two examples you provided (STP and initial BC is correct for muzzle speed 223=.225 and 308=.496).
What I gleaned from this chart is that the break even point for comparing these two rounds is 630 yards. Beyond 630 yards the 308 and the 175 clearly have the advantage in trajectory (no consideration of energy).
I you inital post I thought you were talking about the same rifle/cartridge and different bullets. Seems you were talking different rifles and cartridges.
I personally consider 500 yards as the general break point for bullet/cartridge selection. Inside 500 yards a light fast bullet (lower BC) probably has a slower heavier bullet (higher BC). That being said, my danger space consideration for shots inside 500 yards would go to the light fast types, beyond 500 and I'll pick the slower heavy (high BC) type.
Of course Aussie is correct in that one must consider the heavy fast launcher like the big magnums, these are the favored better choice but the down side is they eat barrels and are a little more user unfriendly.
For your stated scenario, I'd pick the 308.
Once again, good topic. There are other things we can consider, target area (vertical size and depth), critters are three (3) dimensional and not like the two (2) dimensional practice version called paper or steel.