A while back I read a Slate article claiming that laboratory mouse strains have over time become optimized for experimental sensitivity rather than for suitability as model organisms, and that this leads to a number of medical fragilities that humans don't have. Particularly in terms of cancer research: the kinds of tumors that pop up in highly inbred short-lived mice apparently don't have a lot in common with human-typical cancers.

I haven't read enough in this area myself to have a very informed opinion, and I can't find much actual research beyond what Slate cites, but it sounds plausible.