Javascript string comparison fails when comparing unicode characters

I want to compare two strings in JavaScript that are the same, and yet the equality operator == returns false. One string contains a special character (eg. the danish å).

JavaScript code:

var filenameFromJS = "Designhåndbog.pdf";
var filenameFromServer = "Designhåndbog.pdf";

print(filenameFromJS == filenameFromServer); // This prints false why?

The solution What worked for me is unicode normalization as slevithan pointed out.

I forked my original jsfiddle to make a version using the normalization lib suggested by slevithan. Link: http://jsfiddle.net/GWZ8j/1/.