Given those two choices, I would take the .270, and load it with bullets that are well-constructed and heavy for caliber. My choice would be 150 grain, at least Nosler partition. Second choice would be 140 Trophy bonded. Both are loaded in the Federal Premium line of ammunition.

I have taken three black bears in Canada. Two were taken with my .30-06. One I used the Barnes X 180 grain bullet in a handload. The bear died with one shot after running about 20 yards. The second killed with the .30-06, I used the Speer Grand Slam 180 grain bullet. This was also a very quick one-shot kill. The third was taken on a hunt this September. Since the primary animal I was after was a grizzly, I took my .300 Weatherby, loaded with 200 grain bonded core bullets made by Kodiak. I was testing them at the time. They worked very well in both animals, but I took a followup shot on the grizzly. After skinning the griz, we decided that the followup would not have been necessary, as either would have killed the bear.

As to your 6.5X55 Swedish Mauser, I am sure you can kill a bear with it. Just be very sure you hit the bear in a good spot with either of the rifles and it will be very dead. Good luck on your hunt.