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.
Karamojo Bell killed elephants with a 6.5x55, however...He decided to use a 7x57 for most of his elephant kills since the 6.5 bullets sometimes bent and didnt go where he wanted them too.