Energy figures are a part of the key - not the whole story. Bullet weight and construction have as much to do with it.
A .50 caliber roundball from a muzzle loader weighs 177 grains and goes about the same speed as the .357 from a rifle. The .50 is considered adequate for deer out to 100 yards. I don't see why the .357 mag shot from a rifle wouldn't be.
As for bullet construction: A .357 soft point is better than a .30-06 FMJ for deer. The FMJ is an extreme example, but it illustrates how KE alone doesn't tell the whole story.
Likewise KE IS valuable. Nobody in their right mind will tell you the .44 mag has it all over the .30-06 because the .44 launches a bigger, heavier bullet.
It ain't the size of the bullet - it's the size of the wound channel. PERIOD.
I think the difference between .430 and .357 in terms of lethal effect is balogny. If the .357 is merely making a .357 diameter hole something is seriously wrong.
I suspect that for hunting deer, the .357 from a rifle will be fine IF YOU CHOOSE THE RIGHT BULLET. Don't use home or personal defense loads! That's when you're flirting with the possibility of blowing away the shoulder but not penetrating to the vitals.
The bottom line is, know the limitations of the gun. Of course the .357 will have more limitations than a .44 will - shot from the same gun.