Being a pistol carbine fan, my vote is on the .44. Some assert that within it's range limitations and loaded hot, the a .44 mag hits harder than a .30/.30. I would never be so bold as to make such a claim on the internet as it always starts an argument. The .44 will also be a lot less expensive to shoot especially if you handload.

You might also want to consider a .357 mag carbine. Very cheap to shoot, especially with .38 spls, negligible recoil, and can be adequate for close range deer when loaded properly (Buffalo Bore).

I have a carbine in each caliber. The .44 mag has plenty of swat, but the .357 is a lot more fun to shoot.