From what i have heard and to go along with what Amy said above, they are specialized feeders.... meaning that just because two are members of the same species (look a like) does not mean that they will eat the same thing. I asked this same question when i got into the hobby...and was given the explanation at the LFS (who sells them for some dumb reason) that no one really knows.... some eat certain types of sponges, some eat specific types of algae... but no one could give me a definite answer. They did tell me that the prettier it is... the more toxic it will be when it dies... that being said i passed on one that looks just like the one you have above, except more purple.
I have, however had good luck with a lettuce nudibranch.... but its actually not really a nudibranch at all, its a slug. My guy lasted for 3 months before he gave up the ghost.... much better than the 3 weeks that the LFS told me they usually last and they are not toxic. Good luck on your search.