Quisquis and quicumque are both described as indefinite (or generic) relative pronouns, and are both defined in dictionaries as "whoever, everyone who...". Is there any difference at all between the two pronouns -- functionally, or in terms of idiom or period?
Well, according to Gildersleeve, p. 59, quisquis is a noun and quicumque is an adjective.
Quisquis is occasionally used as an adjective, but not in classical Latin. Occasionally, also, but rarely in Cicero, it is used for quisque, quidque.
The fact that he says this (while saying nothing in the same vein about quicumque) suggests to me that the reverse is not true—that, in fact, quicumque is used as both an adjective and a noun.