Mrs Uncle Phil and I did this trip a few weeks ago on our tandem, and we camped most of the time, stayed with WarmShowers folk once. (We completed the circuit by going up the coast to Whitehaven and doing the Reivers Route to Newcastle and then back to York-ish).
If you're carrying camping kit, you may not want to squeeze it into three days. We staged it:
Brid-Yorkish (spent the night at home) 130 km
Yorkish - Pately Bridge 107 km
Pately Bridge - Settle 47 km (but some serious climbing)
Settle - Morecambe and on to Silverdale 68 km
As for which bike, I'd opt for the hybrid if you're camping. You might be able to cram camping gear onto a road bike, but load-carrying isn't what it's built for and you'll probably be more comfortable and enjoy the ride more if you take something with fatter tyres and a more relaxed riding position.
If you opt for the credit-card-and-toothbrush option, road bike.