My preferred method would be to sort each array.
Then just compare with a single loop:
If (string A > string B)
move B
else if (string A < string B)
move A
else
Same - record, and move A and B.
You can use Array.Sort to sort string arrays into order:
string[] st = new string[] { "qwertyuiop", "asdfghjkl", "zxcvbnm" };
Array.Sort(st);