The Model 29 saved Smith & Wesson via Dirty Harry. It was also developed partly due to one of my heroes, Elmer Keith. Additionally you can load it all the way from a .44 Russian to 300 grain grizzly killers. The classsic lines of the revolver is defined by the 6 1/2" Model 29.
I'd have to agree with the 29. Have a 19 not a 29 but the arguments which list the wide variety of loads which the 29 will handle simply put it ahead of the 19 by far.
Since no handgun will get a check mark in every category, got to go with the column with the most.
Had a good look at Elmer's 4 inches in Las Vegas during the antique arms show. I'm still not a big fan of the 4 inch 29 preferring a slightly longer barrel on my .44 magnums. Of v=course that is just me.
I do prefer my guns in calibers beginning with 4 but given the restriction in the OPs post I have to go with the 19. Of course my old 4 inch .44 Special with the lighter contour of their barrels are still just that, special.
M29 for me. I really like carrying the M19 but when a shot must be taken without hearing protection the short barreled 357 is brutal. For me the 44 not so much. The only dangerous four legged animals I have is livestock, but if needed for that chore I feel better with the 44. I do handgun hunt and while I don't doubt the 357 works on deer I have never used one. The 44 has always worked well for that purpose.