I admit to being divided on the topic. Looking at my gun collection I have equal numbers of rifles in both calibers. Those in .30-06 are all US military rifles (1903, 1917, and M1 Garand) while the rifles in .308 are a couple of hunting rifles as well as a FAL assembled from a parts kit. I did have a couple of .30-06 hunting rifles but they have been converted into other calibers (9.3×62 and .338-06).
Vortex Optics through their Vortex Nation Podcast did a video comparing the two rounds including testing them on blocks of ballistic gel.
I do have some criticisms of the comparisons. For example, when comparing rounds for penetration they should have used the same grain weight bullets. In their first penetration tests they compared a 180 grain .30-06 to a 150 grain .308. To me, this is an invalid comparison given the 30 grain weight difference.
With regard to accessibility, 96 factory loadings in .308 versus 94 factory loadings in .30-06 is a statistical tie in my book. One loading not mentioned was the Remington Accelerator round in .30-06 which used a plastic sabot to hold a 55 grain bullet. Turns out Remington made these in .30-06, .308, and .30-30. While not currently being manufactured in factory ammo, hand reloaders can still make these cartridges. E. Arthur Brown Company offers the plastic sabots along with a seater die to allow you to load your own. While still kind of a gimmick given their accuracy, there was a thought they could penetrate Level IV body armor. According to this test, it didn’t despite speeds of 3800+ ft/sec.
In the end, there really is so little real difference between the two that you can’t go wrong with either cartridge. I would feel comfortable using them on anything from deer to moose to most African plains game.