Easiest way to look at it. 308 is equal to the 30-06 to 150 grains. 165 and above, 30-06.
A popular misconception that’s easily countered when comparing the realities of both cartridges. So I'll level this playing field. Use SAAMI’s documents with data from hard-mounted 24" test barrels with the same bore and groove dimensions and measured peak pressure levels for each. Simplified, here’s what’s in print from them:
.30-06, peak pressure of 60,000 psi
110 gr. bullet, 3300 fps
125 gr. bullet, 3125 fps
150 gr. bullet, 2900 fps
165 gr. bullet, 2790 fps
180 gr. bullet, 2690 fps
200 gr. bullet, 2540 fps
.308, peak pressure of 62,000 psi; +2,000 psi
110 gr. bullet, 3150 fps; -150 fps
125 gr. bullet, 3030 fps; -95 fps
150 gr. bullet, 2800 fps; -100 fps
165 gr. bullet, 2670 fps; -120 fps
180 gr. bullet, 2600 fps; -90 fps
200 gr. bullet, 2440 fps; -100 fps
If the .30-06 was loaded to 62,000 psi, its bullets would leave a little bit faster increasing the muzzle velocity gap between these two cartridges.
Note that the first .308 Win. rifles had a standard, long action but a spacer in the back of its staggered box magazine and an extended rib on the extractor to stop the bolt about a half inch further forward. Winchester Model 70's.
In the middle 1960's, given an option between either cartridge, top ranked competitors chose the .308 because of its better accuracy and ease of shooting accurate. The most accurate .30-06 Garands and bolt action rifles shot about 30% more accurate after rebarreling to .308 chambered ones of the same quality using the same quality ammo. That improved accuracy resulted in too many unbreakable ties on the 60+ year old targets so the NRA reduced their scoring ring sizes a few years later.