Sometimes you don't care if there are any empty subdirectories, so the following variant tests if there are any files in the directory or its subdirectories. So it will only look for files! Empty directories are ignored, and subdirectories are recursed through to find at least one file.

I made it generic, so we can toggle this on and off.

Set checkForFilesOnly to true to only look for files.
Set it to false to look for any files or directories (like the previous version).

function isEmptyDirectory(aDir:string; checkForFilesOnlys:boolean = false):boolean;
var
  SearchRecResult: TSearchRec;
  FoundAFile: boolean;
begin
  FoundAFile := FindFirst(IncludeTrailingPathDelimiter(aDir) + '*', faAnyFile, SearchRecResult) = 0;

  while FoundAFile and
        ( DirectoryExists(IncludeTrailingPathDelimiter(aDir)+SearchRecResult.Name) and
          ( (SearchRecResult.Name='.') or
            (SearchRecResult.Name='..') or
            (checkForFilesOnlys and isEmptyDirectory(IncludeTrailingPathDelimiter(aDir)+SearchRecResult.Name)) ) ) do
      FoundAFile := FindNext(SearchRecResult) = 0;

  FindClose(SearchRecResult);
  Result := not(FoundAFile);
end;  

function isEmptyDirectory(aDir:string):boolean;
var
  SearchRecResult: TSearchRec;
begin
  Result := FindFirst(IncludeTrailingPathDelimiter(aDir) + '*', faAnyFile, SearchRecResult)<>0;

  while (SearchRecResult.Name = '.') or (SearchRecResult.Name = '..') do
    Result := FindNext(SearchRecResult) <> 0;;

  FindClose(SearchRecResult);
end;