EAD is always better
you need to stick on to H1 only if you plan to bring your spouse in H4 (for the first time). With EAD, you can switch employers without any problem. You have to proactively renew EAD, since if your EAD expires and you do not have the next EAD, you cannot work legally.
Travel with AP is not a very big issue. With EAD you can also take up a part time job, work in other MSA, whereas you have to amend LCA everytime you go from one place to another. EAD is definitely cheaper overall for companies, since the burden now falls on the candidate.