Retina is a good example of this. Zebrafish can regrow damaged retina, but while mammals have the same stem cells (Muller glia), they dont repair the retina, but form scar tissue. There is a lot of research and I think they have managed to modify rat genome, so that their retina has showns some repair abilities. The problem is that it often causes tumors.

I have other retina permanently damaged, and suffer from double vision when looking small objects like text.