This is what I found from murthy.com (
http://www.murthy.com/rumor.html). It is from 2003 and i don't know if anything has changed since then. it says that one is preferred to use H1b stamp.
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Chat User : If someone uses advance parole (AP) during the I-485 stage INS may respond with an RFE or transfer the case to a local INS office. INS does not like people at this stage to use AP. Posted Feb 25, 2003
Attorney Murthy : We have never heard that before. One is legally allowed to enter on the AP or the H1B. If one entered on the AP, then that person is considered to have been paroled into the U.S. and not legally "admitted," which has its own legal consequences. If the I-485 is rejected, for any reason, then the person is no longer in status, but if one entered on the H1B, then one has the backup H1B status. Each status has its own advantages and disadvantages, but INS does not issue an RFE or transfer the case merely by virtue of having traveled on AP.
Rumor : If one has a valid H1B visa from the employer, and is waiting for approval of I -485, s/he must use Advance Parole to travel abroad and reenter. Posted Feb 03, 2003
Clarification : If a person has an H1B petition approval and the H1B visa stamp in the passport which has not yet expired, the advance parole (AP) is not required. There is a potential risk that the employer may withdraw the job offer when the person is traveling abroad. If this occurs, s/he will be stuck abroad and will need to have a new employer file a new H1B petition. There is also a risk that the green card will be approved while the person is out of the country. In this situation, the H1B becomes invalid and generally cannot be used to reenter the U.S. Filing and obtaining the AP enables one to return even if the sponsoring employer decides to revoke or withdraw the H1B petition or the green card is approved while the person is abroad.
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