In 1903 the 30-03 was developed to shoot a 220 gr bullet for the military. Shortly after being introduced the military decided 220 gr was just too heavy and they changed to 150 gr bullets. In order to work better with the lighter bullet the cartridge case was tweaked very slightly and became the 30-06 we know today. The existing 30-03 rifles were modified to work with the new cartridge. The original loading was a 150 gr bullet @ 2700 fps
Savage introduced a short action hunting cartridge in 1920, the 300 Savage that would match the 150gr @ 2700 fps. By the start of WW-2 the 30-06 military load had been increased to 2800 fps
By the 1950's the military was looking for a smaller cartridge, Winchester modified the 300 Savage to create the 308 Winchester and it matched 30-06 speeds of 150 gr @ 2800 fps. It was introduced to hunters and as a military round at about the same time.
As a military round the 308 was an experiment that didn't really work as well as hoped. It was still too big and had more recoil than they wanted. It found it's niche as a hunting round, as a military sniper round and in machine guns. The 308's advantage in accuracy is real, but not enough for typical shooters to ever notice.
With the best loads available today a 30-06 will push a 150 gr bullet to 3100 fps, a 308 can reach 3000 fps. That 100 fps advantage to the 30-06 does get a little larger as bullet weight goes up. By the time you get to 200-220 gr bullets the 30-06 has closer to 150 fps advantage.
As a hunting cartridge the 308 has several advantages. The 308 is only about 3-4% slower, at normal ranges no game animal will notice the difference. But it uses about 20% less powder and with about 20% less recoil than 30-06. That recoil difference adds up after firing a lot of rounds.
It also allows the use of lighter, more compact rifles. The difference between long and short action rifles alone is 1/4 to 1/2 lb. Plus other weight savings practices allow a 308 to be built much lighter. My Kimber 308 is still under 6 lbs including optics and mounts. Even if you could get a 30-06 that light, recoil would just be too much. My sub 6 lb 308 has recoil almost identical to a 7.5 lb 30-06 and is not bad at all. Recoil from a 7.5 lb 308 is virtually nothing.
The 308 can be used with heavier 200-220 gr bullets, although it is rarely loaded with bullets heavier than 180 gr.
In the real world the 30-06 has a razor thin advantage in range. About 50 yards all things being equal. The bullets trajectory are pretty darn close, but once a bullet slows below a certain point expansion on game becomes questionable. The 308 has what it takes out to at least 400-500 yards. Most people can't shoot that far with anything.
I started with a 30-06 way back in the 1970's. It is a good round, but I would not advise a new shooter to buy one. The 308 comes close enough with a lot less recoil. In fact modern bullets and loadings have made the 308 much bigger than needed. If you discount big bears the 6.5mm cartridges are more than enough and an even better target round. If you do include the big bears even a 30-06 is borderline. You really need 2 guns anyway if you ever plan on hunting brown bear in Alaska.
Oh btw, if you check to see what reloading dies sell the most; 30-06 surpasses all the others in annual sales for many years now. The allure of the 06 is it's been around since 1906, and is the basis for comparison across the board; It's just as good as an 06-or-it's more powerful/flatter than an 06. the 06 is never a bad choice.
