Use of AP and EAD have different impact on h-1.
It is clear that if you use EAD, then h-1 is gone.
If you use AP to enter USA, even though you don't have a valid visa stamp on the h-1, your h-1 or h-4 is still good.
Keep in mind that you need to have different documents to enter the country, stay in the country and work in the country.
The h-1 allows you to stay in the country and work in the country. The visa stamp allows you to enter into the country. You can use AP to enter into the country and still be in h-1, h-4 status to either work or stay in the country.
Once you use EAD then the h-1 is not valid anymore and you have to come in and out on AP.
lawyers have covered this a few times. Once visa validation ended in USA, many have suggested that if you go out of the country you can come back on AP without invalidating H-1, h-4.
below is an excerpt from what is commonly referred to as the "cronin memo".
http://www.shusterman.com/cronin51600.html
4. If an H-1 or L-1 nonimmigrant has traveled abroad and reentered the United States via advance parole, the alien is accordingly in parole status. How does the interim rule affect that alien's employment authorization?
A Service memorandum dated August 5, 1997, stated that an "adjustment applicant's otherwise valid and unexpired nonimmigrant employment authorization ...is not terminated by his or her temporary departure from the United States, if prior to such departure the applicant obtained advance parole in accordance with 8 CFR 245.2(a)(4)(ii)." The Service intends to clarify this issue in the final rule. Until then, if the alien's H-1 or L-1 employment authorization would not have expired, had the alien not left and returned under advance parole, the Service will not consider a paroled adjustment applicant's failure to obtain a separate employment authorization document to mean that the paroled adjustment applicant engaged in unauthorized employment by working for the H-1 or L-1 employer between the date of his or her parole and the date to be specified in the final rule.