The easiest (and fastest) way is to compare the revision numbers of the files, as branching and tagging will not change them.
If you follow this path, you are not checking for identity, but if file was changed in branch, which usually is more important.
So it will report a false alarm, if somebody commit a changed to a file and later reverse merge it back to the old revision. To avoid this, you can diff files which have a non-matching revision.
You can get the revision numbers of all files in head revision by
svn ls -vR REPO_URL/path/to/file
or in nice xml by:
svn ls --xml -R REPO_URL/path/to/file
If you know,that the path to the file(relative from trunk) is unique in the whole repository, you can use grep for getting all branched files:
svn ls -vR REPO_URL/ | grep /path/to/file/without/trunk
Then you have all infos there and just need parsing..(but svn ls -vR REPO_URL/ is really slow)