Disclaimer: I've been using Macs running OS X for work and privately since 2003. However I do use Windows occasionally, and find the current Surface tablets running W10 pretty darn useable.
Having said that, I experimented with Miracast about a year ago and found it underwhelming. Easily a notch or two below the Apple Airplay solution, and even Apple is not perfect. Running full-screen video at 1080p is a little jerky, and this is with a 2 x dual-core Xeon "Trashcan" MacPro on an AC wireless network talking to an Apple TV.
The problem with either solution is that it basically copies screen memory over the wireless network. It leaves the heavy lifting to the application, network streaming, buffering, decoding, rendering etc and then takes the resulting bitmaps and sends it to the device connected to the remote display. The article referenced calls it "HDMI over wireless", and it's worth pointing out that the data rate on HDMI is in the multiple gigabit range. So either solution has to do some compression before sending it over WiFi, and that uses a lot of processing power on the sending device, pushing phones and tablets to their limits. It does work locally without a working Internet if the source is on the device.
In comparison Google Chromecast uses a different method (leaving aside the experimental mirroring from the Chrome browser). The phone or tablet simply points the Chromecast device to the source of the video and decoding takes place on that device. After that the phone/tablet is merely a remote control. It only works with content that has an application/website supporting Chromecast, and obviously requires a working Internet connection.
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