EAD/AP vs. H1
Getting an EAD and using an EAD are two entirely different things. Using an EAD means working based on that EAD and that means when you join any company, signing I-9 form in which employment eligibility is based on EAD. The person can change from H1 status to EAD status by contacting their HR department and filling I-9 form again based on EAD.
Similarly, getting an AP and using an AP are two entirely different things. Using an AP means going out of US and showing AP to enter the US as a parolee instead of showing the visa to enter the US as a non-immigrant. As parolee can't work in US, he/she should get EAD before traveling on AP. Receiving AP is just addition of one more document in your file.
So just receiving EAD/AP does not change the non-immigrant status in any way and he/she is still on H or L status. Thus the person is either in EAD/AP status or in H/L status.
As long as the person maintains the H/L status(H/L status not expired and H1/L1 holders not working for any other employer other than sponsoring employer and H4/L2 holders not working at all), he/she can travel outside US and come back with out the need for advanced parole even after applying for adjustment of status. The person can enter using his/her non-expired H/L visa. The person needs to carry his/her "original" I-485 receipt otherwise serious delay at the airport may be caused. For valid H/L visa holders, there is no need to apply for EAD to continue working after coming back to US. This rule is effective July 1, 1999.
If you are not planning to travel, or work part time for another employer, then there is no reason to apply for an EAD. On the other hand, there is no harm in applying for advance parole and an EAD and there is no reason to try to maintain nonimmigrant status after filing for adjustment of status, unless of course 6 years limit on H/L visa is about to be reached and that the person has no option other than to work with EAD/AP. Please note that it is possible to get your H-1B visa approved for more than 6 years in some cases depending upon your employment based green card processing status. Please refer to the appropriate section on H-1B visa page to find out more how you can extend your H-1B visa for more than 6 years, either 1 year at a time or 3 years at a time.
If you opt for EAD/AP, Spouse(and children, if any) acquired after using AP can't join on H4. Can't resume H/L status after I-485 denial, if any. But you can work for more than one employer, and spouse can work. So it is up to you to decide whether to remain in non-immigrant status or to be in EAD/AP status.
In general, if the person is married, he/she may want to apply for EAD for both of them so that spouse can start working and he/she can also part-time work for other employer, if he/she wishes. If the person is single, he/she may want to maintain H/L status so that he/she can bring his/her spouse on H4 if he/she gets married before adjustment of status application is approved.
Some H-1B professionals use EAD(and terminate H1B) on purpose to save H-1B time so that if something happens with the current employer, they be able to pick up the remaining period of the 6-year H-1B limit through another H-1B approval with the new employer. But that H1 approval would be new H1B and not transfer of H1B and hence subject to annual H1B visa.