I definitely don't want to be cynical, because that's not what you need right now. I just wonder what you changed about your style of parenting between the two children, because if you didn't change anything, then it's no wonder your 13-year-old is behaving in a similar fashion. Now, to the present.
You need to be strict and consistent. Consistency is the key. Do not tolerate disrespect. Figure out what your child LOVES--sports, TV, the computer, Play Station, the phone, sleepovers, vacationing, or whatever. The next step is to TAKE THAT MESS AWAY when your child acts up and DO NOT give it back until your child behaves. For instance, you tell your child, "I want you to clean you room." Your child yells, "I don't want to!" You say, "If your room is not cleaned in one hour, you are NOT watching any television for two days (or whatever)." If it's not cleaned, keep your word; otherwise, your child will continue to play you.
I think 13 is too old for spankings, but I think taking away privileges is the KEY, because they need to know that you are in charge and that you will not tolerate disrespect. Empty threats will only make it worse, and I'm not even kidding.
Let me know if you want to talk anymore.