The .223/5.56 won’t outrange the .308, but the AR platform is more accurate at most competition distances.
The first time I became aware of just how much better the heavy .223 bullets do over the .308 bullets was when I shot and old syrup cooker which looked a bit like a WWI Helmet lying on it’s back.
I shot it with both an HK-91 with German surplus ammo and the Colt H-Bar with a 20 inch barrel. This was at a range of around 600 yards. It was easy to hit with either gun but the H-Bar shot flatter and it put holes through the cooker. The .308 just put a dent in them.