The most obvious difference between hosted and on-premises e-mail models is the amount of control that you're allowed to (or required to) exert over your e-mail systems. When you host your own e-mail server, you have more control over your data, which can be a good thing or a bad thing, depending on the resources your organization has for keeping your data secure. For highly regulated organizations, data may have to remain on-premises for compliance purposes. An on-premises e-mail system also allows for a greater level of customization, which could prove crucial for companies pursuing technologies such as unified communications, in which the mail server becomes tightly entwined with complementary communications services.
Of course, surrendering control and responsibility over the particulars of maintaining e-mail services-either as a means of freeing up IT to pursue other projects or to relocate an essential service to more capable hands-is itself the primary value proposition of hosted e-mail.