I watch both and have each on DVD. I'm glad AMC staggers the seasons - spreads out the viewing nicely.
Like AndrewC, I'm all over advertising history, so Mad Men has solid appeal for me. Plus the whole time period of the Sixties with all the various references to events and culture of that era fascinates me. Definitely more soap-opera than Breaking Bad, but lots of good stuff there.
Breaking Bad has been absolutely mesmerizing. I'm sucked into each and every episode, rooting on Walt and Jesse, and great characters like Saul Goodman (s'all good, man!), Gus, Hank, and Skinny Pete! Lots of tense episodes ("One Minute" comes to mind right away).
Try both, of course. If I had to pick one, though, it would be Breaking Bad.