First up you guys need to move into the 21st century and use SAAMI transducer pressures not CUP. Yes both cartridges are older than most of us but using modern measurements where possible is probably better and more accurate. SAAMI MAP using transducer measurements is 60,000 psi for 30-06 and 65,000 psi for 270 Win. This brings 270 Win pressure advantage to ~8.3%
Next we can't stop at peak force we need to get to acceleration since velocity is ultimately what we are after and we need take into account the mass of the projectiles.
For a fair comparison I would suggest we should use two bullet that are exact copies of each other just scaled (up/down) from the other to the appropriate caliber. ie the proportions and features would be the same. If we accept this assumptions of exact scaling of the projectiles then a 180gr 30-06 bullet using classic scaling (ratios of the characteristic length cubed) would weight 130.9gr if scaled down to .277. Sort of freaky there ain't it.
Using these weights we would find that the peak acceleration for 30-06 is 5.59x10^6 ft/sec^2 where 270 Win is 6.74x10^6 ft/sec^2. So 270 Win has a 20% peak acceleration (at peak pressure). This advantage stays the same as long as the bullets are scales of each other. 220gr 30-06 = 160gr 270 Win, a 150gr 30-06 = 109 gr 270 Win etc.
For the same pressure behind each bullet 270 Win would have an 11% acceleration advantage over 30-06 when using projectiles of the same proportion with respect to caliber. Mass goes with the cube of the caliber were force is only going with the square of the caliber.
30-06 270 Win
MAP: 60000, 65000
diameter: 0.308, 0.277
area: 0.074506, 0.060263
force: 4470.361, 3917.083
Mass: 180, 130.9362
Acceleration: 5.59E+06, 6.74E+06