Dedicated microscope digital cameras typically cost more for less resolution, but they have the advantage of being directly controlled by a computer.  They typically provide a better preview image, often with focusing aids, and the ability to acquire the image directly into various imaging software though a TWAIN or plug-in interface.
They are also recommended for their versatility, being useable both on and off of the microscope, and for the ease with which they can be moved from one microscope to another.