It sort of depends what you mean by "priority."
The private check-in ("Flagship" in AA parlance) is in the same location in T4. It's restricted to:
- International or domestic 3-cabin first class passengers (currently that's JFK, HKG and LHR only, from LAX)
- Executive Platinum traveling internationally, in any cabin
- ConciergeKey
- Oneworld Emerald (not available within US, Canada, Mexico (except MEX), Bermuda, Bahamas or Caribbean)
- American Five Star Service customers (a paid service)
If your travels are not in one of those categories, the remaining premium check-in space is located adjacent to the Flagship entrance. If you're facing the Flagship room, that'd be the set of doors on your right (west).
Just to clarify OneWorld Emerald (non AA) can access Flagship checkin regardless of itinerary. It's only Exec Platinum that is limited to international destinations.
Here's the explanation from AA:
oneworld Emerald: You can use Flagship® First Check-In if you’re flying on any flight operated by American (regardless of cabin).*
*American Airlines AAdvantage Executive Platinum customers traveling solely on North American itineraries do not qualify for Flagship® First Check-In access. North America is defined as the United States (including Hawaii and Alaska), Canada, Mexico (except MEX), Bermuda, the Bahamas and the Caribbean.