Choosing between these two great calibers would be a hard one to make. Given the game you will be pursuing, my choice wouldn't be so much determined by performance, as these are both fully capable of handling such game at any reasonable distance. I would probably choose the good old 6.5 Swed. because it would be the only one in camp, and I've never owned one.
As for flexibility, both the 6.5 Swed. and .270 Win have bullets available from 90 to 160. Standard Cup-core and premium bullets are available as well as varmint specific bullets. The 6.5 (.264) bullet will have superior BC and SD as that of the same weight .277 bullet. However due to the higher operating pressure of the .270 Winchester, it is able to drive its bullet much faster than the mild 6.5 Swed. The difference is great enough, even with the superior BC, the 6.5 Swed. can't catch the .270 within normal hunting ranges.
With that said, charts are just that. I believe people put far to much emphasis on the "Holy" ballistic charts. If you do decide to go with the Swed. I believe you will find it performs better in the field than what the charts say it should.
Still my vote on this one goes to the 6.5x55 Swedish Mauser.
Flinter54