By default, Subversion tends to regard UTF-16 files as binary. It assigns them a MIME type of application/octet-stream. As a result, when an attempt is made to merge a change from a branched version of the file, there is always a conflict that must be hand-edited.
However, there is a solution. By giving the UTF-16 files a correct MIME type, SVN is able to perform merges just like a basic text file.
The required MIME type is one of
depending upon whether the encoding is LittleEndian or BigEndian respectively.
To set the property, use a command along the lines of
svn propset "svn:mime-type" "text/plain;encoding=UTF-16LE" *.utf-16.txt
I have found that this works with the (command-line) SVN version 1.6+ clients on both Linux and Windows.