roc1,
Yes there is a difference. Your question, is it enough difference to matter?, is very subjective.
My personal opinion is that 600 yards and under, the difference between cartridges is actually quite minimal. A 223 pushing a 77gr SMK will hold right up there with a 308 pushing a 175 SMK or a 6.5 Creedmoor pushing a 140gr SMK.
Beyond that 600 yard mark, is when the higher BC of the 6.5 bullets really starts to show a marked advantage in long range, as evidenced by the usage in F Class (along with 6 and 7mm bores).
Of course, at the last F Class nationals the scores dropped hard for the F Open class when the wind picked up, and the scores for the F/TR guys shooting 308s remained about the same. The guys shooting 308s ALWAYS have to account for the wind, and so they were more consistent in the wind. The folks shooting Open class are used to high BC bullets going fast, so don't have to take the wind into consideration as much.
But inside of 600, I wouldn't hesitate to reach for a 308, or a 223.
Jimro