Internet and Network dependent - Let me be very clear about this. Hosted systems are a viable option IF and only IF you have (or intend to have) a quality managed network! Voice traffic is very susceptible to network delays and congestion. Experience either or both of those and your experience will not be a good one.
Trust Factor - Let's face it, not everyone is comfortable having their telephone system sitting in the infamous "cloud". If you don't have a certain level of comfort with the company you are considering providing your hosted service then don't even consider it.
High Availability - The Internet is good and getting better all the time. At the most however you can expect no more than a 99.9% uptime on a hosted solution. Comparably this would be 99.99 or even 99.999% with regular carrier lines and an in-house system.
Requirement for analog devices - If your business still utilizes analog devices then be cautious when considering hosted. SIP to Analog adaptor devices will be required and will add an extra layer of complexity.
As I said every business is different and a Hosted Telephone System is not a fit for every business. The best advice I can give if you are seriously considering this move is to call and talk to a company that offers both technologies not just one or the other. This should increase your chances of having an engaged discussion with a knowledgeable sales engineer who will consider your business needs and look at both options.