This is the working parts of the code, I'll leave it up to you to to test for valid files, for valid content and End of File (EOF) for one or the other file.
StreamReader readFile_1 = new StreamReader(pathToFile_1);
StreamReader readFile_2 = new StreamReader(pathToFile_2);
string inputString = readFile_1.ReadLine();
string[] dataFile_1 = inputString.Split('^');
inputString = readFile_2.ReadLine();
string[] dataFile_2 = inputString.Split('^');
string valueFile_1 = dataFile_1[0];
string valueFile_2 = dataFile_2[0]; ;
if (valueFile_1 == valueFile_2)
{
}
else
{
}
Good luck.