I thought I might as well add my own expirience 
Why I started using XNA:
XNA was just the only? option at that time to make games with C#, and I was just getting into doing more advanced programming. Back then I pretty much only made games with GameMaker 8, and my programming language knowledge was limited to C#, C++ and JS (and of course GML).
Why I started using MonoGame:
In 2012 I decided that I wanted to try out Linux, and part of the tools I was using did not work on it. Now of course I did not just straight up switch to it, it just seemed like a fun thing to have installed on the side, but the more I used it, the more I liked it so eventually I was more on Linux than on Windows and I needed to find some new development tools to work from it.
Most of the tools I wanted to find a replacement for already had something decent, however game dev tools were really Windows only back then, except XNA which had MonoGame project allowing it to run from Linux. As such I just jumped at using it.
Unfortunately, it was missing the pipeline tool on Unix systems, but I was pretty determent to use it so I made my own in a couple of days (no, seriously, made my own: MonoGame Pipeline Tool Mac and Linux ). After that it didn’t take long to get all the remaining parts working (besides effect compilation) and I was happy with using MonoGame ever since.