I've been playing around with a stock NEF 20 gauge lately trying to get some slugs to hit close to where the bead says they should.
To make a long story short, we're talking about 3/4 ounce or so of lead doing 1500 FPS or better.
If my math is right, that's about a 330 grain bullet. I can't see it not having enough power to stop a deer or black bear.
As for accuracy, I have only been working at 25 yards. I'm still "adjusting" things so going farther would serve no purpose to me yet.
Still, out of a stock NEF youth model 20 gauge with a modified choke and a plain bead sight my groups actually look like groups. I have had some cloverleafs with some of the slugs I've tried.
The results are similar with my 12 gauge Mossberg and cheap Remington Sluggers. The only difference is that with my unchoked Mossberg's 18" barrel and plain bead, slugs hit about 5" high at 25 yards and about dead on at 50. Again, I can get groups. I would be willing to try a shot at a deer with it at 50 yards but I'd limit myself to about 70 yards max with it. Even that would be pushing it. The plain bead just limits my confidence for hunting. But for defensive use, I'd bet that 100 yards is pretty realistic.
IMO, the 20 gauge will be adequate if you respect the limitations of slugs, which are going to be about 100 yards max for hunting. One advantage of the 20 gauge is that the lesser recoil will allow you to shoot more before your body tells you it's time to go home, so you should probably be able to become a better marksman.