One of the main reasons is the resolution that computer monitors offer. Whils both will do HD the computer monitor will offer a higher resolution than a tv. Plus you can select from a list of resolutions to adjust to a situation so you have more choices.
A lot of peopledo use tv's for a monitor and seem to be satisfied so if the situation calls for a budget decision then you do have a choice.
monitors and tvs may display images slightly differently due to the arrangement of the rgb pixels or in some cases the addition of yellow pixels. i have found that text is easier to view on monitors and video looks better on tvs but only slightly so and only on certain panels. i have yet to find a concrete source to quote on the exact differences.
as far as having a choice in resolutions: you should only use the native resolution. some monitors and some televisions will not display a video feed in an unsupported resolution and some will autoscale the image. it can be hit or miss.