It is always better to go to the consulate for stamping. However, you should keep your non-immigrant work visa status until the day you get your green card status as a back-up in case their are issues with your green card status. Don't provide too much worry about going to the consulate because an H1B is a "dual-intent" category. If you go into the United States on Advanced Parole you will probably get a "pending Adjustment of Status" and then your employer will not be able to change you back to H1B status.