They're both very strong, and function similarly since they both have long ranged physical ults (though MF's is obviously superior because AoE), magic damage slows and a reliable long-ranged poke. I prefer Cait just because I freaking love using her E, and her traps are a godsend for defense. If you have a tanky support, MF would be the better choice. If you have a Janna or Sona or something, Cait would be better.
Oh, and MF deals extra magic damage on her autos, but Cait has dat crit, so they kinda balance each other out. I'm not intelligent enough to do the math to decide which is better though.
I've turned many games around all because I catch multiple enemies in MF's ult. Usually if they're low you'll kill them, and even if some of them live they'll be low enough to easily clean up. The hardest part is getting good positioning and keeping the enemy off of you long enough for a full channel so good teammates are required.
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Miss Fortune is strong, and if you're used to Ashe then she's only easier to play, TBH. Just keep in mind that she can't escape very well at all, so you want to make sure your support knows what they're doing. She rules with supports like Blitz, Thresh, Taric, Sona, etc that have really good stuns/grabs.
Caitlyn is good too, and is a bit more safe due to her long range and net escape. Much easier to last hit with as well. Caitlyn/Nidalee is probably one of the most frustrating lanes I've ever played against.
MF just has a much stronger team presence due to her ultimate - her AOE slow with her E isn't too bad either.
Cait is really easy to get used to because, well, she's simple as hell to play.
MF is a lot harder to get used to but she's one of the "trinity" right now, although I don't think there's a definite trinity like there used to be. She has probably the best teamfight of any ADC right now, Varus is the only one that comes close.