1) Pixel density.
2) The TV will have muuuuuuuuuuuuch higher input lag. On some TVs it can be in excess of 200ms, compared to 10-40 on monitors.
3) Defects become very noticeable and far more likely, such as back light bleed, or stuck/dead pixels.
4) Speed. It's really hard to find TVs that are able to run at 1080p/120Hz+, typically only found in very specific 4K TVs. On top of that, they generally are only able to display that using HDMI 2.0, which is only found on the newest NVIDIA cards. Things like Displayport or even Dual Link DVI are far more universal on PCs.
What's your budget?