I have both except my Smith is a 4" M29.
Most of the guns described in the previous posts are not what I would call sidearms. Long barrels, scopes, various sights, etc, are all mechanisms to try to make a pistol competitive with a rifle for hunting. A little carbine would be easier for me to carry than some of these huge hand cannons.
Elmer Keith, who took many, many head of big game with his sixguns, never (to my knowledge) hunted with a pistol.
As far as Redhawk vs. 629 goes, you can't go wrong with either one. I have shot my Redhawk a lot more but I've owned it a lot longer. My Smith, with it's 4" barrel, compared to the 5 1/2" of the Redhawk, is every bit as accurate. Either, with my junk reloads using home-made wheel weight bullets, will shoot minute-of-washing-machine groups at at least 200 yards from a plain old standing position. We have shot and hit things at distances that astonish many people. 55 gallon drums across a diagonal 20 acre field can be plunked more often than not with a little practice; this is not particularly hard to do even with open sights. Fit and finish-wise, the Ruger seems almost crude in direct comparison but as far as function goes, it's a toss up with durability "probably" going to the Ruger, mainly because of it's locking system. But very, very few people are going to wear out a Smith.
Most people want to turn these things into cannons, but if you load to about the 1200 fps level, they are very comfortable to shoot, even the 4" barrels. 1200 fps is more than enough to take big game up to 150 yards or so and more velocity only serves to flatten the trajectory slightly--it doesn't materially increase the killing power and the muzzle blast and recoil is much worse.