my boyfriend did the three peaks last year - its still definitely a cycling event - its not the same route as the running route - its a lot longer with linking road sections thrown in.
my chaps got 2 brothers, one who fell runs and rides - and regularly wins the three peaks (til last year where he came second) and the other who's taken up fell running in the last few years - i thought like you the fell running would out - but my fellers cycling pipped his bro's fell running (ooh the family rivalry).
you do have to do carries up each hill, but then there's the "run down" vs. "ride down risk puncture" decisions, and the rocky ride nightmare of pen y ghent lane as a descent