incompatible
"It's not just the different ways they take input that makes the two incompatible."
Is it not rather the very fact that both take (even require) input, that makes them incompatible?
Both are designed to be given some data, and then do something with it.
For a system to be compatible with Siri or Watson, it would have to be capable of coming up with a question that it wanted an answer to, without any prompting, and to be able to do something with the response, other than interpret it as a question.