I tend to agree that statistics is more employable than applied mathematics.
I have a PhD in pure mathematics with an MS in physics, and my experience in hunting for industry jobs is that a lot of employers (though certainly not all) think "math" guys are smart but have a hard time believing they can solve practical problems. They don't seem to have the same assumptions about statisticians. Whether these assumptions are reasonable or not is besides the point - it is an empirical fact. (Of course...who can blame them? Most caricatures of mathematicians show them as squirrely, irritable, reclusive waifs who have a hard time communicating, wear the same clothes every day, and keep nasty, filthy offices where they routinely flail about in an intellectual dreamland.) Sure, pure math is a harder sell than applied math, but applied math is a harder sell than statistics.
My doctoral advisor always told me: "If you can compute, and you can do statistics, you'll never want for a job." Browse job postings at your favorite online job site - you'll see he's not bluffing. I really should have listened to him!
The takeaway is this: if you can somehow double-major in applied math and stats (as others here have suggested) with a concentration in computer science, you should be hot to trot when you land on the job market. I don't see the current obsession with "big data," and people who are facile with statistically analyzing data, going away anytime soon.