Here is a quick comparison of proprietary technology vs. Asterisk:
Your switchboard, e.g. 3x8, only allows 3 incoming lines and 8 outgoing lines. If you want 9 lines you have to buy an expensive proprietary card in order to add more lines. This is called vendor lock-in and is how switchboard companies used to make money.
Voice mail included
Need to buy expensive proprietary card in order to get voice mail
Need to buy expensive proprietary card in order to get IVR
Open interface to all telephony functions
Most traditional switchboards don't have APIs (Application Program Interface) that allow you to communicate with the system. Some do have APIs but they are so difficult to use it makes them useless.
Easy to set up and administer, web-based administration possible
Difficult to set up and administer. You will have to pay some socially challenged switchboard engineer a lot of money to do anything out of the ordinary
Music on Hold can be MP3
Music on hold sounds like jingle bells or there is only a line out jack, so the music on hold runs on a separate system from your switchboard
Open standard, compatible
Proprietary systems are designed incompatible with other systems because this way the telephone company keeps you "locked in"
Lost cost - based on standard PC hardware and uses the Linux operating system