String directory = @"C:\Whatever\";
String[] linesA = File.ReadAllLines(Path.Combine(directory, "FileA-Database.txt"));
String[] linesB = File.ReadAllLines(Path.Combine(directory, "FileB-Database.txt"));
IEnumerable<String> onlyB = linesB.Except(linesA);
File.WriteAllLines(Path.Combine(directory, "Result.txt"), onlyB);