At the proper range, and bullet placement, I don't think the 44 will be a detriment.
While I haven't shot anything with the 44 yet, I have carried it a few times after bear. Plus seeing how close I was to and elk, and a moose this year I think the 44 would have been fine. While I was carrying my 444 at the time, the 44 could have taken the game. Both were not legal to shoot, but you get a great perspective of how close you can get. My first year elk hunting, and I had a 5x5 at 35 yards. I stopped the moose advancing at 65 yrds because I had no larger trees to hide behind if he decided to come in hot. He was a 9x7. Both encounters made for some great video's after I determined they were not legal to shoot.
You should be fine for any deer to 150-200m and most anything else out to 100m.