What programming language should be used to develop Bitcoin exchange software? Why? I've only heard PHP is terrible (e.g. in the context of Mt. Gox) and a more efficient/more security-oriented language would be preferable for matching orders and account security. Which programming language, and due to what reasons, would be better?
There is no possible way of knowing what are the technologies used by the exchanges. 

C++, C# and C have been typically used by the financial and trading software industry as they can be optimized for low latency / high frequency behavior needed for real-time trading. Java, F#, Python, VBA, Haskell as well as other programming languages have also been used but it all comes to a matter of a personal taste, what technologies you or your team are familiar with, what open source (or not) modules are out there that will prevent you from reinventing the wheel and much more that are out of the context of this forum. 

Another way to get an idea for the technologies used by an exchange is to spy on its job adverts. Still, what you'll get might not be accurate or it might refer to another or new product or service of that exchange, or even a migration of the existing technologies towards some other but still you'll get an idea.