I've asked the exact same question over at AFTVnews (sorry, I'm not allowed to post links).
I also found this comment at the Amazon Developer website (again, sorry, I'm not allowed to post links):
"How Basic Edition Differs from Gen 2
From a hardware perspective, the specs for Fire TV Stick Basic Edition and Fire TV Stick (Gen 2) are largely the same except that the Basic Edition doesn’t ship with an Alexa Voice Remote. Fire TV Stick (Gen 2) is available in US, UK, Germany, Japan, and India, whereas Basic Edition is available outside these areas in more than 100 countries or territories (see the full list here).
The user interface for Basic Edition is also simplified in some ways, making it more of an app-centric experience. For example, the “Recommended By Your Apps” rows that is normally populated through Recommendations isn’t shown on Basic Edition. The tabs on the top row are simplified, and you find apps by browsing the available categories rather than using search. Customers can set their default language as Spanish, Italian, French, Brazilian Portuguese, German, or English."
So it seems the hardware is "largely the same", but the user interfaces are different.
As of today, I haven't found how to convert or flash a Fire TV Stick (Gen 2) into a Fire TV Stick Basic Edition.