A big difference between a monitor and HDTV is response time (aka input lag): the amount of time it takes for a pixel to change. The higher (slower) the response time, the more 'behind' you are with the real image.
Generally, TVs have a higher (slower) response time than monitors. This gives the feeling of input lag since there's a delay between your input (e.g. clicking your mouse to fire) and the TV showing the resultant image.
Whether or not this a problem for you is another thing, but I thought I'd mention it

Also, and this is just an assumption, TVs probably aren't as easy-on-the-eyes/as sharp as monitors when it comes to displaying text. TVs are made for showing mostly movies/tv shows, where small text is probably never displayed. On the other hand, monitors are made primarily for desktop use (where text is everywhere) and so are probably going to display much sharper text.
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