Both sentences are correct and mean the same thing in all contexts as far as I can see.
He wanted to know how you were doing. The normal rules of reported speech are used here - wanted and were doing both occur at the same time. Compare:
He wanted to know if I was British. There is no suggestion that I am not British (and British nationality cannot be revoked, or lost). The speaker and listener both know the rules of reported speech so there is no misunderstanding.
However, at times confusion can arise if the tenses are always moved back:
The radio operator said your husband is alive is a better way of reporting matters than The radio operator said your husband was alive.
Arguably, saying He wanted to know how you are is more effective than the alternative as it is very clear.