2004 infiniti coupe automatic 60K miles
Rear sounds like a plane. It is louder than my radio and stock exhaust.
Same sound at every speed. I jacked the car up and shook the wheel. Absolutely no play at both sides.
I noticed there is a click sound coming from the differential when spinning the wheel.
I'm looking for a new or better-than-stock differential.
Should I sill check if the bearings are worn?
Please help.

 

Check your wheel bearing hubs. Most likely inner bearings are out.

 

If you hear the sound of grinding, high pitch noise, or even airplane noise. It's the rear hubs. Change them both together you'll feel a huge different in acceleration and response in the back end.