I love my 77/44. I haven't worked up any loads for it, but Winchester SP box of 50 shoots great. I hit five diamonds out five @ 50 yards, and I doubt this rifle will see much action past 100 yards.
Where I take it 50 yards is the limit of sight. They are great hunters, but don't expect to win any contests. LOL Yes, I did hit all five diamonds that were about the size of a nickle at 50 yards last time I went to sight the scope in for the Winchester 240 grain SP factory ammo.
I like to load .44 Mag. I love my Ruger SBH 5.5", but this bolt gun didn't like the cowboy loads that the SBH did. So I have to see if it will shoot the 240 XTP with 2400 as good as my SBH.
The .44 has some recoil from the light carbine, but the difference in size of the bullet holes it makes is enough to choose the .44 over the .357, and a 77/357 will have the same limitations on distance as the .44 Magnum. So flatter shooting isn't a deciding factor here I wouldn't think. Also, the recoil isn't bad at all, and if you are shooting an animal you will not feel the recoil anyway. It will shoot specials just like the .357 will. Practice with specials, and hunt with Magnums.
Whatever the .357 does the .44 does at least 1/3 better if not more. Provided that you can hit what you are shooting at.
All said and done though if I were stuck on .357 it would be a Marlin 1894. If I wasn't stuck to pistol calibers then a .22-250 would be my choice for pig hunting with my wife.