If you go with COBRA, make sure you really do have access to the same kind of provider network in your new state. Even if you have, say, Blue Cross Blue Shield in both states, the way your current state plan works may be different from your new state -- and the new state may only cover emergencies. In my experience, it would be very unusual for an employer plan in one state to have anything resembling similar coverage in a new state.
The move WILL allow you to get an ACA plan though, assuming you don't take COBRA or if you give up COBRA before you move. The ACA plan is likely to be way cheaper than COBRA also, depending on your income.