I think observing them come and go is a useful tool to understand their impermanence and often, their insignificance.
I use them interchangeably but I would say that feeling is more the physical response, emotion the psychological response. Not my technical area though :)
I also start to have the feeling that most of the time they are insignificant...
I try to be observant when I can but the brain can be very tricky some times :)
It can indeed, it is a wily one at protecting its imaginary ego.