Your tv will upscale the incoming signal, so it is shown at the tv's native resolution, your average computer monitor does not do this, but stretches the image instead.
This means that if your Hanspree has a 1920*1080 pixels native resolution and you feed it a 720p signal, it streches the image to almost double size. When monitors run images at a lower resolution than their native one, the image will look blurry and unsharp.
Televisions tend to cost far more than average monitors, so the built in scaler will almost always do a better job with upscaling to native resolution.
This problem will dissapear if you're able to feed your Hanspree a signal that matches it's native resolution.