What is the asymmetric feature on the rear of a Sukhoi Su-47?
The Su-47 has two tailbooms of unequal length outboard of the exhaust nozzles. The shorter boom, on the left-hand side, houses rear-facing radar, while the longer boom houses a brake parachute.


Source: Wikipedia

Related: What is this part between the Su-35&#39;s jet exhaust nozzles?

Note: Your second image is mirrored. Here's a real photo with the right (starboard) boom being the longer one:


  
  Su-47 (aka S-37) in lead, also notice the tail numbers of the formation (no mirroring); source: wikimedia.org