Just opinion, so it's worth what you paid, maybe!
I really don't think that the .357 Max gives up very much to the .44 Mag, if you only consider whitetails, even though your whitetails get quite large, comparatively.
Now, it has to be a given, that you reload for the Max, and use bullets 180gr and up. Trajectory will be slightly flatter, and recoil will be less. Plus, bullets are marginally cheaper. :?
That said, if you don't reload, the .44 is the way to go. Ammo is accessible almost anywhere (a big factor with the max), there are lots of loads to choose, from very mild .44 special loads to full-house factory & custom loads like Cor-Bon & Buffalo Bore 300+gr heavies.
Also there others to consider. What about the .45 Colt? 10mm? .45Win Mag? There are lots of choices. Don't ya just LOVE Contederitis??? :-D
Personally, I use both the .357 mag, and the .44. Our deer are smallish, and both perform well. I use 180gr in the .357, and 240 and up in the 44. Both are cast bullets. Just depends on which I decide to pick up that day.
Again, JMHO.................