The both cancel claim and have a new effect, though without the word "instead" are they not technically claim replacement? They cancelled claim, and then have a new effect?
The curiosity comes from, since they both cancel claim, can you play 1 vs the other since, technically, it seems claim is cancelled after the first one is played - leaving nothing for the other to respond to.
Such as: Player 1 wins a MIL challenge against a Martell player (P2). P2, is the first player and gets first response. They play Red Vengeance to cancel the claim effect and initiate a new effect.
Can P1 now play BSobG?