In both the CF and British forces, the adoption of the 5.56 platforms changed the marksmanship standards upward from the "bad" old 7.62 days.
I was in the CF infantry during the transition, and our old "good" days on the range became "ok" days behind a C7. While I wouldn't want to be hit by either, I guess the best argument could be made for the 5.56 since more trigger-pullers could hit the target more often. The various effects of terminal ballistics are immmaterial if the round doesn't hit anything but dirt.
I trained the first batch of British infantry recruits to start out with 5.56mm and the SA80. We believed the SUSAT* optical sight was also significant, as its forerunner the SUIT** had improved shooting scores on the range with the SLR (L1A1 version of the FN FAL in 7.62) but proved unpopular in the field because the mounting system wasn't very good for holding zero.
Trials had indicated marksmanship would be improved with the new weapon system so the range practises and marksmanship standards for the new weapon system set higher expectations than the SLR and 7.62mm. The first course of new recruits exceeded these higher standards by a good margin. By the end of my posting at the Depot the standards had been revised to require even higher scores and even then the success rate was higher than with the old weapons.
Although the optical sight was credited for much of this improvement, I heard that in the support arms where the SA80 was issued with iron sights only (and as a bullpup it had a shorter sighting plane than the SLR) the recruit depots also reported better overall accuracy, so the lower recoil cartridge was definitely significant.
Before my posting to the Depot, my battalion had an operational tour in Belize, for which we converted to the AR15, and that also bore out that the lighter rifle in 5.56mm improved marksmanship scores.
And as you say, it doesn't take two more enemy combatants to carry away the casualty you missed with a 7.62mm. I liked the FAL, it's a very robust, reliable rifle and that's very reassuring, as is the power of the 7.62mm. But the big picture truth is the 5.56mm in a lighter rifle is better overall.
*SUSAT = Sight Unit, Small Arms, Trilux
**SUIT = Sight Unit, Infantry, Trilux