The only reason that I could think of for anyone wanting to hunt Big bears with a 308 would be if that was the rifle they had and got a chance to do a bear hunt. If they did use it they would have to be more concerned with the range of the shots and know what their gun is capable of. However I would bet that the 30-06 has probably killed more Big bears than all other calibers combined. This because its been in the game fields where the big bears live for 100 years now. The 308 with 180-200 grain bullets within it range will do about anything the 30-06 will do. I woullld prefer the 45-70 and thats what I have used most for hunting all bears. However I have used the 30-06 as have many others on this site and had good results doing so.