Why the big device? Why not a little HDMI dongle you plug in? Is there any difference in functionality?
Samsung's Allshare Cast looks like is only compatible with Samsung Android devices (newer ones at that). So Miracast and Intel's WiDi are essentially Wireless HDMI, sending video and sound wirelessly to the screen. So yes, it works as if it is plugged into the Screen, works well for presenting Decks or watching Video Content. I wouldn't use it for productivity or Web surfing as there is a noticeable lag between the Surface and the Screen, and this has been true all of my devices.
I saw in the other thread you were using B@LLS OUT with Max Brightness and MAX CPU so 3 hours under that load is quite good....Miracast can impact battery, if you are planning this again, it may help if you get a Power Cover, it should get you 4-6 hours under the same conditions...