Funny thing is, both the Virginia and Yasen class are 'modernized' cold-war designs. The Virginia, a lower cost version of the Seawolf class, optimized for 'green water' ops. Reports say its slower than Seawolf and cannot dive as deep.
Yasen class was designed in the cold war, delayed and re-designed with more modern equipment when new funding came available nearly 20 years later. Like most late soviet era boats, she's probably fast and capable of diving very deep. She's also probably slightly noisier than the Virginia.
Sensors edge would goto Virginia class. If she's expecting trouble, she'll likely detect the Yasen first.
BUT
Weapons edge would goto Yasen. Super-cavitating rocket torpedoes such as the Shkval or stand-off ASW missiles, the Yasen can 'put a warhead on the forehead' further away and faster than the American.
So while Virginia detects the Yasen further out, she's got to manuever into a better range for her ADCAPS to have a chance. In that time, the Yasen might get a sniff of the Virginia. If not, she'll hear the launch transient and snapshot something back. So, a gunfight for sure.
What its going to come down to is each sub's (and crew's) ability to evade. It's Virginia's fight to lose. She just wasnt fully optimized for deep ocean ASW fights. She can certainly do that, but the class was built to also do other missions.
If the Seawolf class had properly been kitted out with UUM-125 Sea Lance, then Yasen loses. So, to make it a fair fight you might say it takes place under the ice cap, thus removing the Russian (and american lack of) stand-off weapons.
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