Having had significant experience with using a hosted PBX and now an on premise PBX, I will relay my experiences here. First and foremost, whatever you decide to do research your chosen service provider(s) before choosing them.

Hosted PBX

A hosted PBX is a PBX that is hosted by the VoIP provider. Typically you would connect your phones directly to the VoIP provider's service via your public internet connection. Some providers also offer an internet termination option that gives you a T1 or similar internet connection that is terminated directly into their data center, avoiding the public internet altogether.

Advantages of Hosted PBX

• No investment in a PBX is necessary.
• Relatively ease and quick to implement.
• If the internet connection is down the provider can be configured to route calls to cell phones or other backup lines.
• Multiple internet connections can be used to provide connection redundancy.
• No need to upgrade the PBX as this is automatic when the VoIP provider upgrades there systems.

Disadvantages of Hosted PBX

• If your VoIP provider is down your phones are down.
• If the VoIP provider has exceeded their maximum number of concurrent call sessions you will not be able to make an outbound call.
• Usually higher ongoing fees. Cost is usually priced per extension which can often be expensive for low volume users.
• Locked into the limits of the hosted PBX. If a custom feature or experience is require this can be expensive or impossible to add.
• • Services like InphoniteVoice can be used to augment your Hosted PBX and provide custom, on demand solutions.
• Additional features usually add to the monthly fees.
• More difficult to switch between Hosted VoIP providers especially if your internet connection is provided from the VoIP company.
• Extension to extension calls routed over your internet connection unnecessarily using bandwidth.

On Premise PBX

An on premise PBX is a VoIP PBX that is located at your site (or your main office). This computer would be connected to the internet and route phone traffic to your Internet Telephony Solution Provider (ITSP) or your traditional trunks (Analog, Digital). Most VoIP PBXs can be configured to do both.

Advantages of On Premise PBX

• Multiple call routes can be created to provide redundant ITSPs.
• Multiple internet connections can be used to provide connection redundancy.
• Total control over the user experience. With the wide availability of tools on the market, companies with engineers can write custom applications to build a complete custom experience.
• Can interface with existing "legacy" phone connections for either primary or backup service.
• Easier to switch between ITSPs.
• Allows for integration with Unified Messaging platforms such as Exchange 2007.
• Usually lower ongoing fees.
• Extension to extension calls stay on your LAN or WAN.

Disadvantages of On Premise PBX

• Upfront costs. You will need to buy and maintain a server and PBX software.
• More difficult and time consuming to implement.
• Requires a more technically savvy staff to configure and maintain.
• If the PBX is down your phones are down.
• May need to pay for upgrades to the PBX. Downtime risk when upgrades are performed.

Choices

As you can see it's not a simple answer whether to choose to go between a Hosted PBX or an On Premise PBX. I will recommend that if you go with a Hosted PBX choose a company that can offer you an internet connection that is terminated in their data center. Using the public internet, at least in my experience, may lead to call quality issues. For our company we used a hosted VoIP provider and were very disappointed. It took us 4 months of research but eventually we decided to switch to an on premise PBX with multiple ITSPs (three actually). This allows us to provide redundancy and elastic capacity. Whichever you decide make sure you do your research. Choosing a lemon is a costly mistake which can leave to less then desirable customer experience.