Can these two expressions be used interchangeably? I'm not sure but if I'm not mistaken "in which way?" is not correct, or maybe I just can't come up with an appropriate sentence.Also I've just checked the definition of "which" and it says that it specifies things from a definite set, so it would be more natural to use this word in an expression like "Which way did he go?" I'm almost sure "In which way is he better than me?" isn't grammatical, at least I don't think I would ever use it over "In what way is he better than me?" I would appreciate if someone corrected me if I'm wrong or otherwise confirm my assumption. Thanks in advance and sorry for any possible mistakes.
Yes, you are correct.
"In which way" could be used, but only when there is an option of a number of specified choices.
"In what way" would be used (as is usual) when the possible options are not specified, and the "way" could be anything.
I am trying to think of a sentence in which "In which way" is correct, but I can't think of anything which isn't hopelessly contrived.