In solidity you can not really compare two strings with each other. You can surely compare them as byte arrays practically comparing the characters one by one, however a more elegant way is to compute a hash of the two string and compare simply the two hashes. Due to the cryptographic properties of the hash functions, the chance to have the same hash of two different strings is astronomical small. An example can be seen bellow:
contract Compare {
function compare (string a, string b) returns (bool){
return sha3(a) == sha3(b);
}
}
