What's your favorite 100-125yds deer caliber?
Since you asked:
I use a 15" 300 Win Mag barrel. Of course, that's a bit excessive for your needs.
Since you already reload for the 7mm-08 and you have experience with the 44, you could narrow your options down to one of those two. Honestly, I think you'd be fine with a 12 to 13 inch 44 Magnum even at those ranges. If you want the 7mm-08, you'll probably need a 15" or longer barrel. Bottleneck rounds start losing a lot of velocity once you start shortening the barrel past 14". I know my 12" 270 barrel loses a heck of a lot more velocity than my 15" 300 Win Mag and 243 barrels. That said, the 12" barrel handles and carries a bit better, although to be fair the 15" barrels aren't all that bad in the field.
Want my advice? Choose the caliber that
you want most.
Or both.