This option is becoming more popular, but I don't think it is for everyone. If you have several small field offices, it may make sense to have the hosted option, whereas with a large headquarters staff, the enterprise model may be best.
The advantages or disadvantages really depend on your organizational structure, your internal IT department's ability to manage an enterprise CRM model and version control. Some vendors touting the hybrid CRM deployment model are stating that the on-demand portion of their offerings provide greater flexibility, speed and disaster recovery benefits than a pure on-premise installation. With both models; however, communication between the vendor and your organization is critical.