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Both are good. 270 as stated will have a flatter trajectory--At 300 yards this is not a issue nor is the extra 100 fps.
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Both are very comparable in terms of power as you've stated. The .270 starts out marginally better but that gap widens as range increases.
Just to put some data on the table for people to see the differences, here's an example. Lets compare a 180 grain in .308 to a 150 grain in .277 I chose these weights as I thought the bullets were most comparable. They have similar Sectional Densities (with the 150 grain having a slight advantage) and ballistic coefficients (the 150 grain in .277 having a slight advantage again-of course this can vary with bullet choice)
They both leave the muzzle with similar energy, with factory ammo. The .308 leaving at just over 2600fps and the .270win @ 2850fps.
@300 yards
.308 2124fps
27.37'' drop
.39 seconds flight time
6.76 inches of wind drift with a 10mph 90 degree crosswind.
1803 ft/lbs energy left
.277 2358fps
22.65'' drop
.35 seconds flight time
5.83'' wind drift w/ 10mph 90 degree crosswind.
1852 ft/lbs energy
so as we can see the cartridges are very close to each other. The .270 having a slight edge @ 300 yards due to it's marginally shorter flight time, ~5'' less drop, ~1'' less wind drift, and 50ft/lbs more energy. Along with the better sectional density of the 150 grain, all these things adding up makes the .270 the "better" cartridge.
The difference is small enough that it doesn't really matter though. Both will be very effective for their chosen job. I'd pick the .270 simply because it seems to be more available during panic times. The .308 is such a common and popular cartridge that many people are shooting it, and therefore buying it. Normally it wouldn't matter but after our most recent ammo shortage, it's easy to see that the .308 may get hard to purchase again. And with it being such a popular cartridge demand will be higher. Supply and Demand: if more people need it and less have it, prices go up. From my limited second hand experience, it seems that .270 ammo is staying on the shelves, even during panic times. The .308 is not.