Scooby, First of both will do the job for deer out to 100 yards. I am going to assume you are looking to buy and don’t already have either of these. If you have a reasonable chance of hunting a shotgun only area then I would lean toward the 20 gauge. If not I would get the 44 no question. I do most of my hunting in a shotgun only area and own 20 and 12 gauge rifled barreled shotguns, so I know how effective they can be. They are accurate enough to take deer out to 100 yards, but I still would prefer a center fire rifle. I have no experience with the handi rifle, but would be surprised if it could not equal (probably not exceed) the accuracy of the typical slug gun. The 44 mag in a rifle is only about 100 feet per second or so slower that a 20 ga with similar weight slugs. The ammo is less than half the price. The selling point for me though would be that I could get high end 44 mag ammo that would equal and likely exceed the ballistics of the 20. An example is the buffalo bore ammo’s 270 grain ammo does 1800fps out of an 18.5” barrel (you should get at least 1900 out of a 22” barrel). And the ammo would be slightly less than the over $2.00 a shot slug gun. I like the idea of being able to shoot a variety of power level (and price point ammo) in one gun. It would be more range time and couldn’t be any less pleasant to shoot than a slug gun. I do not enjoy shooting mine, they are simply tools. Personally I would get the 44 in a lever gun, but they do cost more, and I get the single shot attraction. I am trying to find an excuse to buy a Ruger no 1, but they are just too expensive for this family man, and I really don’t need another rifle. Just don’t tell the wife I said that. Whatever you get, I hope you enjoy it.