On the category CatSet of usual set based categories, there is a "folk" model structure, as described on the first page of Model structures for homotopy of internal categories by T. Everaert, R.W. Kieboom and T. Van der Linden. Namely: in CatSet, ws are weak equivalences, cs are functors injective on objects, fs are functors with the lifting property for isomorphisms. wfs are then precisely the full faithful functors surjective on objects.

Is there's any nice sense in which this model category structure on CatSet is unique?