I had exactly this just recently. We were descending to a level 1000’ above a lower aircraft. We got an RA (AP TCAS worked very well, thanks Airbus). The other aircraft said they only received a TA. Both A320s, no other TCAS traffic within 20 NM. I’ve also been on the other side where another aircraft got an RA and we only got a TA with TCAS blue on the PFD. Whatever is supposed to happen, it certainly seems like just one aircraft can get an RA.