(Update, 20.4.2015: As it turns out – this post is not entirely accurate, as pointed out by Johannes Sebastian. Please read the next post to learn more about which parts are, and which aren’t correct.)

Control Add-ins written in C# are not cross-version compatible. You cannot use an assembly compiled for 2013 R2 with 2015 (or the opposite way around, or any other version combination for that matter) without recompiling it with correct extensibility framework assembly reference.

Control Add-ins written in JavaScript don’t have to be recompiled, are mostly interchangeable, and are (so far) guaranteed to be forward compatible. You can always use a version built for 2013 R2 in 2015. You can use a version built for 2015 in 2013 R2, but the opposite way around is only true if you don’t use any of the new JavaScript extensibility features not supported in earlier versions.