One of my shooting buddies hunts up here in Alaska solely with a contender, and primarily with a 309 and 375 JDJ. From his experience, the 309 is a poor choice for moose, and marginal for larger black bears.
You are also sacrificing 100 fps by going to a 12" barrel, and those rounds need all the speed they can get for consistant bullet exspansion.
Both rounds are accurate, and preduce a good deal of recoil, the 375 definately comes back in your hand.
My personal suggestion would be a 6.5 JDJ for white tails, and a 375 for the big stuff.