My conception of what philosophy as a discipline was was largely the continental tradition (including of course the ancients and early moderns that are embraced to some extent by both traditions). As someone who had never really studied it, philosophy was for me characterized by the likes of Plato and Nietzsche, and I wasn't particularly interested in that stuff. I took an intro ethics course late in my (first) college career, and loved it, but thought it was too late to change directions.
After graduating I was listening to a lot of courses that are available free from the likes of Yale and Berkeley (which are awesome by the way if you have broad interests), and stumbled across John Searle's Philosophy of Language class. I was blown away. I never knew philosophy was anything like this, and I've been all-analytic since. Went back to do an undergrad phil degree, and now I'm in an M.A. program.
I avoided continental stuff in my second undergrad, but I just finished my first continental seminar, and I'm sure I made the right choice. We read Nietzsche and Foucault and some others, and while there was some interesting stuff there (mostly in Foucault), it doesn't grab me the same way analytic does, and I can't stand the writing style. I may dip into it from time to time (like I said, I have wide academic interests), but it's not something I want to devote a significant part of my life to studying.
I'm not sure I buy this idea that the distinction between these schools is breaking down. My department is quite pluralistic - we've got a couple analytic people, a couple continental people, a couple who do applied ethics (which I sort of think of as outside either of those two, but I'm not all that familiar with the field, so I could be wrong), a eastern phil prof, a christian phil prof, a phil of race prof, etc. Still, I get a bit frustrated with the way philosophy is done in my continental seminar, and the continentally oriented students get a bit frustrated with what we're doing in the analytic seminar. There are of course going to be people who like both, but my admittedly small sample leads me to think that's a minority.