That is kind of a trick question.
Pro's to keep it on - It keeps the computer at temperature and ready to go. This prevents contracting and expansion of parts, more specifically on the soldered connections. However, the Con is that it is harder on the power supply to keep it going consistently without the power supply getting a break. It also is harder on the fans, which are constantly running.
Pro's to power down - The whole computer gets a "break" and cools down. It also saves power. The Con is that this causes contracting of the heated components, and eventually causes wear over years of cycling on and off.
As far as whether to keep it on or not, it is really a matter of preference, as any wear would take years to show, and...