I would say that we would use crossbreed as a noun. This dog is a crossbreed. And, we use crossbred as an adjective. It is a crossbred dog.

Crossbred is the past tense form of the verb crossbreed. If they are appearing as characteristics in a list or something, they can potentially mean the same thing, except one would be the past tense verb (crossbred) and the other would be the noun form (crossbreed).