Edit: Here is example code that detects the different Windows Phone updates (for update 1, 2, and 10. You can edit the javascript.)
In Update 2 it looks like they removed support for the 2011 style flexbox (with ms prefixes) which can be tested for by the following code:
'msFlexAlign' in document.documentElement.style
This returns true for Internet Explorer 11 Mobile Update 1, and returns false for IE11 Update 2. Here is a jsbin test.
Note I found this by using the Modernizr 3 cow tests, and comparing the Results for update 1 and the Results for update 2. There was only one difference, the flexboxtweener value changed from true to false.
Edit: If you need to detect Update 1, then a way to detect the difference between IE11 on WP8.1 and WP8.1 Update 1 is that 8.1 Update 1 (And Update 2 as well) supports document.ontouchstart which you can test using 'ontouchstart' in window. However beware that an App on Windows Phone 10 (10.0.10586) it reverts again if using a WebView (A WebView uses IE11 and 'ontouchstart' in window === false!!! Arrrgggh).
Edit: If using a WebView in an App compiled for target WP8.1 on Windows Phone 10 (Windows 10 Mobile 10.0.10586) then it uses IE11 and an App does not use Microsoft Edge! WTF: That version of IE11 returns true for 'msFlexAlign' in document.documentElement.style
so it seems that changes for Update 1 and Update 2 were lost or reverted in WP10 - ouch. You can detect IE11 on WP10/W10M (Update 3 ;-|) because it has "Trident/8.0" in the user agent whereas IE11 on WP8.1 has "Trident/7.0". You might only look for the difference if the user agent contains "WebView/2.0" (although https://msdn.microsoft.com/en-us/library/hh869301(v=vs.85).aspx also mentions "MSAppHost"). Other things may happen if using Settings | Desktop Mode (which amongst other changes removes "Windows Phone 8.1" and adds "WPDesktop" to the user agent), or if using X-UA-Compatible to change document mode to < IE11). Windows docs are "In apps compiled for Windows 10, WebView uses the Microsoft Edge rendering engine to display HTML content. In apps compiled for Windows 8 or Windows 8.1, WebView uses Internet Explorer 11 in document mode." (CAVEAT: Our experience was that apps compiled for target Windows 8 use IE in document mode 10, and a new empty project for target 8.1 had to be created and everything copied over from the old project before it would use IE11 in document mode 11).
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