richms:
Displayport gives a nice clear compression free, lag free image on multiple screens, or 5k on a high res screen, just like a desktop PC.
Wireless mirroring works for showing powerpoint presentations and movies. Cant work on it because of lag, cant have dense text on it because of compression. Also ok for mirroring gameplay so you can show it to others or capture it on a HDMI capture box, but you cant play it on the mirrored ipad to appletv output because of the lag.
And the apple HDMI output from lightning thing sucks hard too. No comparison to native video output.
DisplayPort also does true 4K @ 60Hz. WiDi/Miracast has 2 big advantages over official Apple TV mirroring solution via another apple device.
1. Extended screen. You can use the second screen (TV or PC monitor) that you are mirroring to as an secondary monitor.
2. No power point required on the wall. Like the official Surface adapter from MS, you plug it into a USB port on the TV or monitor and it powers the WiDi/Miracast adapter so it's also very portable to carry around.
Edit - Not including new HDMI spec 2.0 for 4K @60Hz