There is nothing wrong with the 16 ga. I used to only have a 12 ga and shot plenty of rabbits, squirrels, birds... with it and yes I have torn some of it up, but there were sometimes that I was glad I had it. If you are looking to get a new gun, then fine. A 28 ga supposedly is the best all around shotgun you can find. However, what you have will do the trick just fine.

I have found with a .410, that sometimes it isn't enough (shooting hare). I can make a good, well placed shot on a sitting target and that blasted hare will get up and run away. Then it is up to the dogs to either catch it or bring it around again. Cottontails don't seem to be so hearty.