Okay, so here's the basic information on both when fed:
: He excels at locking down a target, and with the long duration on his shield, so long as the enemy carries aren't fed all to hell, you can soak a large amount of damage with the shield itself. His ability to guarantee a knockup on a specific target is also fight-breaking. He won't do any special kind of damage, on the other hand. He really just doesn't have damage skills, but he makes up for that with a stupid amount of cc.
: Draven puts out damage. Draven puts out a stupid amount of damage. Draven puts out damage so quickly and so stupidly high that he can oneshot squishies if sufficiently ahead, and I know of no adc save a Quinn with the drop on him that could actually duel him, purely because of his ridiculous damage. He doesn't fall off lategame, and in fact scales into lategame better than most adcs. What falls off lategame is his utility: he has a slow/knock-side, and that's it. He doesn't even have a passive after hitting full-build, because extra gold does nothing if you don't buy anything with it. That's why people think he falls off: passive becomes useless. Despite having no passive, he still does very well late game.
Tradeoffs of each champion
: He has a weak early clear and his ganks are far from guaranteed. Nautilus excels in situations where he can countergank, entering a situation with the ability to peel someone off his team with an easily hit anchor. However, if you miss the anchor, that's a lot of his "free kill" pressure gone, because he has no gap closers. If you want to gank as Nautilus, it's best to wait for the enemy to burn any sort of dodge ability first, then anchor. This usually means just walking into lane behind them and getting up close to snare with his passive.
: Draven is so mechanically difficult to play that a bad Draven is totally ignored after dying once. Nobody has to care about him because he isn't a threat. All of Draven's power comes from his Spinning Axes, and if he drops those, then he loses a massive chunk of his strength as an ADC. In teamfights, the mark that shows where the axes land makes it easy to toss cc where Draven HAS to be, forcing him to either take cc (which is terrible, as an adc) or lose damage (which is terrible, for Draven.) He needs a high level of mechanical skill to function against a decent team, but he'll steamroll anyone that can't deal with him.