Bowser vs Falcon is a tough matchup, but it's doable. It gets more difficult the safer the Falcon plays. There's two ways a safe Falcon will mess up Bowser, baiting moves and pushing Bowser to the ledge with aerial threats. Because Falcon has more mobility and that ridiculous dash grab, he can dash towards you and back off right before getting in range to bait a reaction from Bowser. Problem is, Falcon can punish almost any of Bowser's moves with a real dash grab. If he can get you to throw out a ftilt, dtilt, utilt, fortress... anything besides jabs, he can get in and punish.
So first off you'll have to figure out what he wants. Is he dancing out of range until you commit to something, whether in the air or on the ground? How does he approach, is it the same every time? Does he mix up dash attack and dash grab, or does he always run in and dash grab? If he never uses dash attack, then you know you can time a spot dodge into something fast (fortress, klaw) to stuff that approach. If you want to get ahead of it, you can throw out some jabs as long as your timing is good enough (consider it a 50/50 if you're just throwing jabs out). You can also use a short hop aerial fair/bair while playing the spacing game against a grounded falcon, as long as you're autocanceling aerials, Falcon has to have pretty good timing to get between a fair to jabs or bair to ftilt.
The reality against great Falcons is, Falcon's jump is his best spacing/threat tool. Falcon jumps high and moves fast enough in the air to use his air jump to get back safely, and his aerials come out really fast compared to Bowser. It's not a great idea to challenge him in the air, generally. Of course, bair will lead to an acceptable trade with just about anything... but it's probably better to see the pattern and catch him as he tries to land - utilt for coverage, run past and pivot grab or usmash when confident.
Most of all, this match really depends on Bowser confidently going offstage for the kill. Falcon's recovery is terrible and predictable. If he is preparing to recover from below you absolutely must run off the stage into a fair. One fair will gimp Falcon and end his stock at almost any percentage offstage. If he manages to grab you with his up b, prepare yourself to tech off the stage, but it doesn't happen that often. Fair has huge coverage and usually beats Falcon's up b. Falcon can live to annoying percentages because of his weight. I've klawed Falcons after 100% many times to my disappointment. He's much easier to kill horizontally than vertically.
That's enough babble about Captain Falcon. Of course, theory doesn't always translate nicely into gameplay. But Falcon is a predictable character outside of two fast moves - dash grab and raptor boost. Figure out the player's dash grab tendencies and the match becomes doable. Until he spikes you during recovery, anyway.
I don't think Duck Hunt would be a good matchup. Falcon is heavy, and DH doesn't have a consistent enough wall to stop Falcon from running through and wrecking it.
Also go here for DI'ing against him:
http://smashboards.com/guides/how-to-di-all-throws-in-smash-4.341/
