Typically, because televisions display the limited 16-235 space, it is better to use the RGB limited mode to send 16-235 to the TV. The image looks washed out due to the change in gamma curve to 16-235 and the settings will need to be calibrated with software like DisplayCal.
If you TV has an HDMI black level setting, make sure this is set to "off" or "normal" while using 0-255. That may eliminate the black crush on that input. Sometimes there is a specific HDMI port on a TV meant to receive 0-255 signals. It is usually called HDMI/DVI or something like that, and will give a better picture with a source like a TV.