Considering that the 308 was developed as a means to reduce individual infantryman's ammo loadout weight and bulk while retaining as much as possible of the '06's ballistic performance, the '06 remains the Big Daddy of the traditional USA service cartridges. I carried and fired both the M-1 and M-14 in the service, then owned an M1a and M-1 in subsequent civilian life. The M1a is gone. There was a cash crunch, and it was the most saleable item in the inventory.
I missed the M1a, but by the time I was in a position to acquire more guns, it was priced clear through my own personal roof.
The 308 did a good job, while it was permitted to; but it was retired long before its dotage by efforts to economize and reduce ammo weight/bulk even more. Can't change history, but that didn't serve my desires for a 308 service-suitable rifle. Slow to awaken to modern products, I finally acquired a PSA PA-10 20" 308, and IMHO, it's at least as good for my personal purposes as the M1a it replaced.
I doubt I will ever part willingly with my Garand.
So where does the 30-06 excel? It does better at the farther reaches of the trajectory, with reduced drop/drift, and potentially more terminal performance (more powder in equals more power out). I'd say the break even point occurs at around 600yd, with the '06 taking over beyond that. I could have the yardage off by about a 100yd or so.
I can't shoot the 300WM due to surgical legacy issues, but would be confident shooting the 30-'06 in situations where the 300WM is customary.
We used to have a 30-'06 exponent here, Userid USSR, who achieved some remarkably effective 30-'06 handloads that bordered on 300WM performance. Sadly, USSR has not been seen on this forum since 2012. Don was a personal friend, and some time before I moved o/o NY, I lost touch.
Greg