As far as I know, you should turn both of them in
However, when you get back to the US it is better off to enter with a valid H-1B status (if you still have it) than entering with the AP and remain in the country as an "adjustee". This is because, in the event that your I-485 is denied for any reason (knock on wood), you may still work under the H-1B status, whereas if you are an adjustee you simply fall out of status under that circumstance. This is my understanding of the process, but you should not take it as legal advice since I am not an immigration attorney.