John,
This is determined primarily by the customer and their specific circumstances. Many just want to offload the admin and management of such systems to someone else and just define what they want out of it. Others will be concerned over the perceived lack of responsiveness to changes from a hosted solution and a lack of control.
With convergence and virtualisation, there is tendancy to centralise the deployment of the physical solutions (hardware) into big data centres and deploy the functionality over the LAN/WAN so who looks after and where it is deploy is fairly unimportant to the business users. Convergence also allows centralised management and control, but with local administrators to handle the specific needs of each business unit to a certain degree.
One determining factor that has become more prevelant recently is security, especially with call recordings and speech analytics (PCI DSS, etc) but even this can be got around in a hosted solution if the correct safeguards are put in place.
Recent experience has seen a tendancy for clients to go with a managed service solution, rather than full hosting - i.e the solution is deployed in their own data centres but managed by the supplying systems integrator or service provider. This seems to give clients a good compromise between offloading totally and maintaing a level of control that makes them feel comfortable that it will work.
Sorry, that was a very long way of saying - "it depends"!
Dave