A 1920x1200 resolution monitor has a higher resolution than a 'Full HD' TV, but that's not really a good thing if you're using it as a TV! More pixels doesn't mean better picture quality, especially if you have more pixels than you need
As 1080p video is 1920x1080, displaying it on a 1920x1200 screen will either involve black bars top and bottom (if you're lucky) or a stretched image (if you're unlucky). Some monitors do not have an 'aspect' mode or similar (where they show the feed in it's native resolution) so they just stretch the image to fill the screen, distorting it at the same time.
There can be other issues too. Personally I'd always go for a TV over a monitor, unless I only had room for one display in my house! I accept it may be a good idea in a small flat or something, but you seem to have plenty of other kit, so I'm sure you can fit a TV in!