function Are2FilesEqual(const File1, File2: TFileName): Boolean; 
var 
  ms1, ms2: TMemoryStream; 
begin 
  Result := False; 
  ms1 := TMemoryStream.Create; 
  try 
    ms1.LoadFromFile(File1); 
    ms2 := TMemoryStream.Create; 
    try 
      ms2.LoadFromFile(File2); 
      if ms1.Size = ms2.Size then 
        Result := CompareMem(ms1.Memory, ms2.memory, ms1.Size); 
    finally 
      ms2.Free; 
    end; 
  finally 
    ms1.Free; 
  end 
end; 

procedure TForm1.Button1Click(Sender: TObject); 
begin 
  if Opendialog1.Execute then 
    if Opendialog2.Execute then 
      if Are2FilesEqual(Opendialog1.FileName, Opendialog2.FileName) then 
        ShowMessage('Files are equal.'); 
end; 

{********************************************} 

{2.} 

function FilesAreEqual(const File1, File2: TFileName): Boolean; 
const   
  BlockSize = 65536; 
var   
  fs1, fs2: TFileStream;   
  L1, L2: Integer;   
  B1, B2: array[1..BlockSize] of Byte; 
begin   
  Result := False;   
  fs1 := TFileStream.Create(File1, fmOpenRead or fmShareDenyWrite); 
  try     
    fs2 := TFileStream.Create(File2, fmOpenRead or fmShareDenyWrite); 
    try       
      if fs1.Size = fs2.Size then  
      begin         
        while fs1.Position < fs1.Size do  
        begin           
          L1 := fs1.Read(B1[1], BlockSize); 
          L2 := fs2.Read(B2[1], BlockSize); 
          if L1 <> L2 then  
          begin             
            Exit; 
          end;           
          if not CompareMem(@B1[1], @B2[1], L1) then Exit;         
        end;         
        Result := True;       
      end;     
    finally       
      fs2.Free;     
    end;   
  finally     
    fs1.Free;   
  end; 
end;