I don't think that anyone has mentioned from what I have seen, forgive me if I missed something in someone's comment, but the most obvious thing to me that supports the general consensus that this is a problem with El Capitan, is that El Cap no longer has the option available in System Preferences/General for anything relating to handoff.
I have always had this option in the past on my MacBook and now that my handoff capabilities do not work, the absence of this selection in Preferences implies that the ability is not even available to me in El Cap. I discovered during researching the problem that the Apple web page for the El Capitan download relating to the Handoff feature states that if the option is not available in your System Preferences/General menu, then your device does not have the capability; HOWEVER, as I said, my device had the capability in the past with Yosemite. Also, I point out that, although I have an older model MacBook, I did confirm prior to the install of El Cap that my MacBook was a supported device for the El Cap upgrade.
Seems as if El Cap has an issue with some devices in not recognizing handoff capability or installing the function properly. Either that or those of us with older MacBooks may be out of luck with handoff capabilities moving forward. Hope that isn't the case.
MacBook Air (11-inch, Late 2010) OS X El Capitan v. 10.11
iPhone 5S iOS 9.0.2 (13A452)