It's well known that a simplicial model category presents an $\infty$-category by the homotopy coherent nerve construction. (I am drawing my knowledge and terminology from what little of Lurie's "Higher Topos Theory" that I know). An obvious question is:
Is it possible for two Quillen inequivalent simplicial model categories to present equivalent $\infty$-categories?
I think the answer should be "yes". Provided it is, what I'm really interested about is:
Is there some way to tell when two model stuctures will in fact yield the same $\infty$-category?