There are a number of concerns in play that must be considered when answering this question. IF you are still a full-time employee in good standing at the H1B employer, and you have a valid H1B visa stamp, or can apply for a new one on a short trip abroad without a harrowing, uncertain and lengthy procedure, then it is preferable to use the H1B visa for travel.
The first reason for this is that under the H1B, you will be re-admitted in valid non-immigrant visa status, which keeps you in status regardless of the I-485 application. The second reason is that under the regulations, you may travel on your valid H1B visa as soon as the I-485 receipt notice arrives, instead of having to wait months for the approval of ancillary benefits. Also, this will usually avoid having to go to Secondary Inspection at the airport upon your return. However, some H1B workers are subjected to extraordinary levels of scrutiny and indeed bias at some airports, particularly information technology professionals working in a consultancy, so the risks of traveling on the H1B visa should be discussed with counsel before you go.
While travel on Advance Parole is possible as soon as you receive the combined EAD/Advance Parole card from USCIS, and using it for travel is necessary when you are no longer working for the H1B employer, know that whenever you present an Advance Parole travel document to U.S. Customs & Border Protection, you will always have to go through Secondary Inspection. In Secondary, the Customs & Border Protection inspectors may start with a presumption that you are inadmissible because of the Advance Parole, and work backwards from there – which means entry coming back to the U.S. will almost always take longer with an Advance Parole than with the H1B visa.
Once you are admitted as a Parolee:
A. You’re no longer in valid H1B non-immigrant work visa status.
B. In order to just stay on payroll at your employer, you will have to present the EAD card and execute a new I-9 form.
C. You will no longer have access to H1B portability, should you wish to change jobs abruptly.