You don't mention what range.

Out to 600m (and sometimes further) my .223 does really well with heavier bullets. It only fails me (or I fail it) at longer ranges.

The .308 does respond well to longer barrels if you load for it, especially when using heavier bullets or you want that extra 100 or 200fps with a lighter bullet.

I use those two calibers and am very happy with their performance. But, age is catching up with me so the recoil with the .308, even with a heavy rifle, starts to bother me after 10 or 20 rounds. I am looking at 6.5 and 6mm choices as well.

Here are some good guides of different target cartridges.
https://www.accurateshooter.com/