Think of the Wireless Display Adapter just as the same thing you would get by having a wired monitor (it includes audio in the stream - you dont need to purchase anything else). You use the normal Windows settings to either extend, mirror or just use the second monitor. I typically sit in my couch and have my coding environment (IDE) open in my Surface screen while I either have video tutorials or browsers open in my living room 55 inch TV.
For entertainment purposes a Google Chrome (they released a new one last week) is good enough. It has apps such as Netflix and it connects to your home router to fetch data, so it doesnt drain your devices batteries. You control it through mobile apps or the Chrome browser add ons.
In the other hand, the Miracast devices do a P2P Wifi connection to your device, it doesnt even need a router. Hence, the battery in the Surface suffers because it is constantly keeping the Wifi connectivity to the adapter. It basically makes up for a HDMI cable not being there, there are no apps or anything like that that could be installed to the adapter.
My experience with the Microsoft adapter has been excellent. No noticeable lags or quality loss. I highly recommend it to anyone that is used to working dual screen and wants to be moving around the house without being constrained to a docking station. If you only want to watch online content on the TV and your TV doesnt have built in apps, get a Chromecast, its only $35 in the US.