Falmer are about the most difficult enemies to sneak up on. I don't know if Muffle will help, but if they hear you, you are detected.
Muffle will. Also invisibility breaks combat with them (which it should not)
Falmer are actually a joke for all my sneak characters- you are having trouble sneaking on them? As a vampire with muffle and high sneak I have stopped "sneaking" altogether recently and just run around invisibile, the silence is good enough to avoid all detection so you can just drop into sneak(at the last second) for an attack, or just start the intiative with a swing.
Edit: I believe there was a thread concerning exactly falmers and detection factors in the spoilers section not 2 days ago. I posted some general stuff.
Edit2: yup- here it is , but it is in the spoilers- beware! :: http://www.gamesas.com/topic/1349067-visual-detection-by-falmer/page__fromsearch__1