That depends on which status you want to be in. Both have their advantages and disadvantages, the H-1 has been approved for a longer period of time so you will not have to go for a visa again, the H-4 validity is shorter so you will have to go for a visa again shortly. H-4 you can work for any employer but processing time for an extension unless its filed with the spouses H-1 takes a long time and you cannot work once it expires. H-1 you can only work for that employer and if you do not work as per the terms and conditions of the LCA you will be out of status.
