Putting aside the nationalistic bashing, I don't see how a Virginia is going to fair any worse at taking out a CBG group than a Yasen, a 533mm torpedo is going to sink a capital ship just as well as a anti ship missile. with the plus that there in comparison, there is virtually 0 active anti torpedo defense other than sinking the opposing sub first or launching decoys and hoping that that works. Again we can go through the whole debate of whether the multi layer missile defense is really as vaunted as it is claimed, but it is clear that a torpedo has to jump through less hoops than a a missile.
Basic physics and probability theory.
The effective range of a torpedo is less than 50 km, and that is in the detection range of any sonar.
It means the submarine has very good chance to be detected and in worst case the enemy will detect it in the moment when it launch its torpedoes, so it will get few ASROC type missile in short notice (in 1-2 minute).
So, it is quite difficult the get close enough , and even if it successful the attack could be the last thing that the submarine did.
The other part is the probability.
The detection range of a sonar is at least 300km against an aircraft carrier.
So, the Yasen can cover at least 36 times bigger are to attack then the Virginia, as a starter.
Means 36 times more Virginia needed to patrol the area covered by one Yasen.
It is exactly the same case why everyone argue about the advantage of the Nimitz class against smaller, non catapult carriers.
Again size and volume of armaments really only matter if one can reliably hit a target, more missiles to lob against a target is better sure. But with every missile fired the chances of one getting detected increases. And unless working in a networked system (which is unlikely given the nature of how subs work) it did be hard for the Yasen to exploit the full range of the missiles).
Quite hard to detect the missile launch from 300km.
Bigger sonars, maybe, but do anyone knows that larger sonars has better passive capabilities because for subs using active sonar is damn near suicide. And again just because a sub is smaller does not necessarily mean that its acoustic tiles will be thinner or the acoustics will be lesser, that will largely depend on design.
You argue with basic physics .
Bigger aperture will increase the sensitivity - it is this simple.
Bigger diameter give more space for damping ,smaller gives less.
Diving deeper is fine and all but that also deprives the Yasen of using its missiles. one of the few advantages it has over the Virginia. And thermal layers works both ways, if it negatively effects the enemy's sonars it will also negatively effect the Yasen's so it's a bit of a double edge sword. Due to the pump jet design there is not much need for the Virginia to dive that deep in the first place.
It is the opposite.
The USA forced to use pump jet because they can't dive deep.
The pump jet decrease the maximum speed ,and most likely will increase the noise above the optimal speed.
The Russians use it on the SSBNs.
Thermal layers can be used to mask the submarine, and the sofar channel gives chance to hear ships far away - and attack them.
Also the Virginia actually cost a pretty penny to build, at 2.8 billion UDS per boat it is actually the third most expensive ship the USN can build currently. Unless the Yasen cost a whopping 5.6 billion USD ( they did have to pimp it out with gold plated tiles for that price tag), I don't see how a Yasen is going to "cost more than 2 Virginia subs")
The Yasen is an advanced version (with VLS tubes) of the Seawolf class (that was designed against the Akulas) , and that had a nice 5 billion $ pricetag.
So maybe three times expensive should be more accurate.
Cost of Virginia is about 2 billion.