Just something to consider because if you shoot a deer with a 44, while the energy may be the same, the volicity of the bullet will be a lot higher at the distance you would shoot with a pistol and more then likely the bullet will open up.
If you fire a 300 grain bullet out of both firearms and the energy is the same at the impact then the velocity would also have to be the same.
The expansion would be nearly identical between the two bullets. Although the 44 may penetrate a little deeper due to the slightly higher sectional density but the terminal results would be pretty much the same. A dead animal.