They'd argue about everything. Actually, I've always pictured Sherlock having a break down like he did in Hounds. This time it'd be far worse, because not sure he could comprehend the universe and the alien beings that inhabit it.
((Let's just combine these shows into one, so that we can have WhoLock. And also, the Sherlock hiatus can FINALLY end.))>> Actually there is one difference it's that in Doctor Who there running from danger while in Sherlock There running to danger.