You can get the mild recoil of the 6.5x55 while using the .270 just by switching powders. Here's an example from the online Hodgdon Reloading Manual: in a .270, 43.7gr of Varget with give you 2700+fps with a 140gr bullet.
The 6.5x55 will also do close to 2700fps with a 140gr bullet and 40+gr of powder. The recoil should be too close to tell the difference, and the resulting trajectory (if you use similarly designed bullets) will be within an inch or two to 400-500 yards.
Score: +1 for the .270 because of versatility, +1 to the 6.5x55 because of "coolness". It's a tie!