20's simply kick @ss..... most of the deer i shoot have been with a 20 using grey box wins and hornady sst's. I have set my wife up with an lt20 rem 1100 having a smooth bore rifle sight barrel an a 26" mod barrel and she has been very successful with it keeping within the yardage capabilities like anything else.
I have been using a win 101 for over a decade as my primary grouse gun, a lot lighter to carry for 5-6 hrs non trail walking including 30 rounds of ammo an outing then the same in 12 i carried before that.
My 20s consist of a womens/youth bps (started deer hunting with this early on), charles daly o/u 28" full/mod, win 1300 xtr with a smooth bore slug barrel a rifled barrel and a 22" vr removeable choke barrel (if i didnt want to pass this one onto my daughter it would be my do all gun nice to carry with the alum reciever), zabala sxs (cheap spanish), and a good old cooey single. All these are great guns but most have their own application as well. If i were to choose one as a do all gun it would be a pump either being the bps or the win 1300 xtr (super smooth action). The one though i have yet to get is a nice A5 in 20 as kamlooky suggests.
I seldom carry any of my 12's anymore and use the 20's on grouse, rabbit, turkey, crows, and deer. Every now and then i use the 1300 with rifled barrel using the 250gr hornady ssts on coyote, they dont much like it (im not into keeping hides).
Great choice of gauge in my opinion just find what fits best for your application(s).