not to be a downer, but just from looking at 8 of my friends who did B.S., M.S., or PhDs in applied math: 5 are unemployed or underemployed.
the three that are employed ended up: Kristin went to grad school for a PhD in meteorology and is now working for NOAA, Becca became an actuary, and Taryn became a teacher at a private school.
The other 5 of my friends who did applied math (who went to UConn, UVa, UMiami (x2), and PSU for whatever level their terminal degrees were) ... none are working in applied math and two are not working at all.
Most of what those guys have told me is that they have had trouble in that:
if they apply for business/management jobs, they don't have the managerial experience / internships / MBA / six sigma / ect...
if they apply for engineering, they don't have the certs
if they apply for programming jobs, they don't have the portfolio / CS degree to get past the HR gatekeepers
Honestly, it's all about networking though. I'm sure if these guys were to really work at it, they'd be able to get jobs, but most of them aren't exactly great socialites. I think they just believed the whole guidance counselor thing that "if you go to college and do well, there will be jobs waiting for you."
Last I heard, Saad may be going to medical school through the army, and Anthony evidently has been working his way up in some bank where he started as a teller after finishing his M.S. in mathematical biology. So right there, two out of the 5 seem to be doing something, the others are just in a rut (either unemployed or working entry level at walmart/starbucks) as far as I can tell from what I can see on facebook, linkedin, and gossip from mutual friends.
Jobs are out there, but eh, no clue if they're any better or worse than ChemE or anything else for that matter. Good luck with your decision though, and NETWORK, NETWORK, NETWORK!