Depends on what do you want
I would not work on EAD unless you can always get an "employment intent letter" from the current sponsor.
Yes, you can work on EAD, but at the time you start, you are loosing your H1 status.
The best way of doing this is to file a H1 transfer, then take care of I-485. It it is more than 180 old, notify INS of a "sponsor change", otherwise you\'ll have to file a new one.