This is a super hot forum debate topic for a lot of car and bike forums…
From what I subscribe to, the coefficient of friction doesn’t really apply to tires in any useful way as it is too simple, only modeling sliding friction and not rolling friction or the effect of deformation(such as while turning). Grip is a function of the mechanical (not just tread pattern, think tire pressure) and thermal properties of the tire along with the riding surface, the weight of the motorcycle, rider, and gear. While the size of the contact patch does not form a direct linear correlation with grip, a bigger contact patch influences the magnitude of the coefficient of friction due to temperature and abrasive effects.
So theoretically it is possible for the narrow tire to have equal grip, but practically, not so much.
Now the real question is, why do we call them tires while the rest of the world calls them tyres??? Where’s the theory on that one!?!? 
