The switch had nothing to do with the .308 being more powerful or having less drop. Actually, it's not quite as powerful and has MORE drop when using heavier bullets.
The switch had more to do with carrying more rounds of ammo for the same amount of weight on the soldier, and some political reasons, and some other reasons I won't pretend to understand.
The 30-06 and the .308 both shoot 30 caliber bullets. The .308 has a smaller case, and therefore holds less powder. BUt it is rated to a higher pressure, so faster burning powders can be used. When shooting 150 gr bullets, the two are identical. The both shoot the 150 gr 30 caliber bullets at the same velocity, so they will have the same ballistic drop. But when you get up to 180 gr bullets, the longer bullets take more powder space, and therefore a higher percentage of the powder space is stolen from the .308 case than the .30-06 case. So the 180 gr 30 caliber bullet can be sent out of the barrel at 2700 to 2800 fps from the 30-06, but can only be sent at 2500 to 2600 fps from the .308. This will cause more drop.
So don't buy a .308 over a 30-06 thinking that you're getting a more powerful cartridge that won't drop as much. That's not how it is. The biggest reason to buy a .308 over a 30-06 is... is... wait. There isn't one.
J/K. It's if you really want a short action to lose that 3 ounces off your rifle. And there is something to be said for that.