Sounds like you were shooting match ammo? Do you also shoot deer with field points when you bow hunt? About the same thing. It wasn't the caliber, .308 and .30-06 are damn near identical in medium weight bullets.
O/P if you have a .308 and are looking for something different a .30-06 ain't it. Yes heavier and louder but that's about it. Tons of neat stuff to pick, a WSM caliber, RUM, .338WM, Weatherby, etc. you want different, go different.
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They differ in 100-300 fps. in all of the "newest and greatest" calibers designed to sell guns and ammo.
There is nothing wrong with the classic calibers with the new bullets.