I remember reading a similar thread to this on the old forum site. I think though I could be wrong, that to maximise your air intake you breathe through your mouth, although some air does circulate through your nostrils anyway.
What the tape thingy does, I've no idea and I've never used one.
Got to admit I wouldn't be able to breathe through my nose when I'm running as it tends to have goo coming out of it (which is nice!)