Twitter provides a means for sharing a message to others in mass and being able to respond back to it. That's the core value proposition and on that basis it competes against Facebook, Google+, Path, App.net, Tumblr / microblogging and a whole host of others that did not or have yet to get very far. That's not to say that these companies would identify Twitter as their target but rather that almost all major social services are centered around a similar idea: the feed.
The question however is their approach to it (Twitter pushed short lengths while Path uses actions) and how people chose to use them (Facebook never wanted to be particularly private, but the amount shared caused people to expect the option). Thus the biggest risk to Twitter is not so much a competitive service doing something a bit better as it is a change in the user and what they want.
Take instagram as an example: while you could call it limited (and I did not list it as a competitor for that reason), the response to a photo is generally many times that of a tweet, even a tweet with the same photo. By operating solely around visuals and by allowing one-way micro-interactions, Instagram caters to something Twitter thought they had themselves... It gave people a focused way to do photos.
In fact I'd argue that Twitter's greatest strength is also the potential weakness: freedom. Facebook centers around a friends & family, Instagram around and interests and affinity but Twitter is really up to the user to define. This is what makes it so powerful but it also creates friction for the new user. This also extends into the power users vs lurkers dilemma but I'm already far enough off topic from your question.
As for Facebook, with over a billion users people may not love the system, the rules, or even the UI but they certainly seem to have figured them out just fine.
But I'm long on both.