I have hunted with several 20 gauges over the years and love them.
With a rifled barrel, good variable scope, a solid rest and shooting the Hornady SST slugs, 175+ yard shots are very do-able.
Granted, I would not shoot at a running deer at those distances, but I hunt mostly out of blinds and stands and a standing, broadside deer at 175 yards is in serious trouble.
The 1187 or 870 in 20 gauge is a safe bet.