I'm not starting to debate whether a monitor would be better than a TV although I prefer using the "right" tools for each task.
There's a simple reason why the image on the TV isn't as crisp as on the monitor. Assuming both are 1080p the pixels on the TV are 18.5% larger than on the monitor. Further, as the viewing distance for a TV is much longer the screen can be made rougher (cheaper, older technology) meaning there's more stuff between the pixels than on a monitor designed to be viewed at an arm's length.
You can think the screen as two million boxes with a colour changing lamp in each box. On a 27" monitor the grid of the boxes is barely visible even with a perferct eyesight. On a 150" monitor the grid would be the size of the mesh used for mosquito nets on windows. Thus, if you want the image on a larger screen to be as crisp as on a smaller one you'd need more pixels to fill the area. That in turns requires more oomph from your video card.