For better or worse, it seems like Twitter and Facebook each want to be the other, possibly to the detriment of each service.
Twitter has been adding more ways to encourage "sharing" (particularly with retweets), something that has traditionally been a strength of Facebook's. Also, Twitter's PR of late appears to be encouraging non-tech users to join by highlighting celebrities and making efforts to be more mainstream. I wouldn't be surprised if Twitter is behind the bulk of high profile actors, sports stars and musicians to recently join, rather than those people discovering the site on their own.
Facebook, meanwhile, seems eager to make new strides into areas traditionally considered Twitter's forte. Rather than being content with individuals and their friends, they have been making large pushes to integrate companies and brands into the site, whereas these "non-people" have been a large part of Twitter for quite a while. Facebook has also been putting a lot of effort into making the News Feed much more real-time (I think their acquisition of FriendFeed is an example of this). In addition, Facebook has pushed their users to be more public (causing some controversy in the process), whereas the vast majority of Twitter users have been posting publicly from day one.
As this happens, I think it pulls each site from their strengths. I suspect that each site would be happy to pull users away from the other, even though I think they can live in harmony quite easily. The way I personally use Twitter and Facebook is that for me Facebook is personal: I only friend people I already know personally, and therefore post things that only my friends would find interesting. On Twitter I look to network: I have no qualms about sharing with "strangers", and in fact I look for new, interesting people regularly. When I post on Twitter I always keep in mind that clients, business partners and customers may be seeing it. (Interestingly, for me Twitter has largely taken the role that LinkedIn used to have.)
In essence, on Twitter I am generally in "work mode", and on Facebook I am in "personal mode". My content on each site reflect this, and I usually have little trouble deciding where to post. If I'm discussing my new hair cut, it goes on Facebook. If I want to share my thoughts on, say, how Twitter and Facebook differ, it goes on Twitter :).
Unfortunately, I don't think either Twitter or Facebook is content to sticking to where they shine and only focusing on core strengths. I suspect both companies get tremendous pressure from investors to constantly grow, and this means finding new users wherever possible. Ultimately, it's a core problem with the investor-focused world in which startups currently live. If you're bootstrapping, growing to a nice, profitable size and staying there is perfectly acceptable. When you've taken in $50 million in venture-backed funding, you'd better be aiming for a huge potential exit, which means keep growing or die.
