Bullets of equal SD/design generally have similar BC, so my guess is .270 would win by a hair given that it will drive bullets of equal SD a bit faster and have less time of flight. Of course there are some anomolies for both where one make of bullet will show signficantly higher BC for similar SD. One example is 130 nosler (SD 242) vs 165 nosler (SD 248) partition federal factory loads:

Load No Caliber 100 Y 200 Y 300 Y 400 Y 500 Y
P270P 270 Win. 0.7 2.9 6.6 12.4 20.2
P3006AD 30-06 Spring. (7.62x63mm) 0.8 3.2 7.7 14.2 23.1

I believe bullet weight does help reduce wind drift, but fatter caliber doesn't help so may offset some in .277 vs .308. You can probably find more really heavy (200+ gr) super high SD/BC (.300+ / .500+) bullets for the .30-06 than you can for the .270 which generally tops out around 150 gr.

Lou