The 308 Win cartridge is popular because of the number of them as a result of the NATO designation. There are many used for match competition. There are many bullet offerings for the .308 WIn.
On the other hand, the 270 Win started life as a game hunting cartridge and was popularized by Mr. O'Connor. Actually I think it was a clunker in those days, but so were most other cartridges of that ilk.
The 308 has many uses as does the 270 Win. However the .308 just ain't as sexy as the 270.
Neither cartridge is a 1000 yard big game getter, in my opinion.
I don't know of a bullet for the 270 Win, currently offered that approaches a bc of 0.600. That is a bummer. The 270 Win will push a 150 gr bullet as fast as a 308 will. Give that bullet a bc over 0.600 and it won't even be a contest.
Come up with a 160 gr offering with a > 0.600 bc and the 270 WSM becomes what a 270 WSM should be. Oops, drifted off there for a bit.
My first "Western" rifle was a 270 Win for shooting everything from chucks to elk. It did well. 90 grain Sierras for chucks an yotes to beyond 400 yards. 130 Sierras for deer. Same for moose. Never did shot an elk with it. Many mule deer.
My first "Eastern" rifle was a 7MM Mauser. The 30-30 of the world. Could only get 170 gr bullets from the factory. Another bummer.