It would have to depend on how much I, as the hypothetical student, have in the martial arts have myself. If I, as a brand new student who doesn't know my ashi from a hold on the ground, were inquiring, I probably wouldn't know the difference between the two and would go with whichever teacher seemed to be closer to what my ideals would be (patient, informative, relaxed but disciplined, etc) and could teach me the most effectively. I would also take into account how the students look and stuff of that nature.
I, as a more experience MA'ist, on the other hand would have to take into account other criteria. If the 10-year teacher who studied under the Head of the system was a "Maurice," if you will (see "Common Martial aRts Students thread in Comedy Cafe, I think) and the more experienced teacher was trained in a very hands on and physical manner, I would take the latter of the two.
All things being equal, I would have to go with the better teacher, not the better pedigree.