Reposting the gif since we finally killed the old thread. That is really nice.
To me, the difference in their reactions is exactly the point. They are two different men. Different times call for different heroes. If Blake reacted in the same way stoic way as Bruce that would have rang completely false...he doesn't have a deep-seated fear of bats. In fact bats probably have more of a positive connotation for him, since they're the symbol of his childhood hero. This ties into what I was talking about in the other thread about how Blake doesn't necessarily have to become the next Batman in a literal sense, but I'll leave it at that for here.