As stated above, my QC2 headphones work fine with my computer, fine with my iPhone 4s, and does not work with my iPhone 6 plus.
Update: I found my Klipsch Image S4 II in-ear buds, and they work just fine. So I guess the 1/8" mini plug on my very old (~9 years now) QC2 headphones is just not compatible with the iPhone 6 plus. Weird, I would think that it conforms to some standard (both the plug and the socket).
Thanks guys for all of your suggestions. Hopefully this will also help the OP with his issue.
//Nuketea