It's interesting that part of the rationale for building huge submarines is that the Soviets couldn't afford American-style aircraft carriers. Then they proceeded to bankrupt themselves making huge submarines.
That fleet can be taken out with a single tactical nuclear weapon.
A nuclear submarine can operate on its own, and carries more firepower (If we count by number of capitalists/communists/unaligned people it can kill) than an entire carrier group.
An aircraft carrier is useful for force projection on the other side of the world, if you are trying to bomb some stone-age savages, or to carry out some gunboat diplomacy to an uppity developing nation. It can't surprise-surface 30 miles off the coast of New York, and launch three dozen half-megaton nuclear weapons at six different metro areas in the span of forty minutes.
The Soviet Union was much more concerned about it's security than it was about power projection. It didn't need carrier groups - it needed a way to guarantee it's safety from nuclear attack, by holding the threat of initially Cuba, and later, it's submarines over the head of the US.
The former USSR's, and today's Russia's foreign policy become a lot clearer when you understand their primary goal - security of the homeland from attack. The country was absolutely traumatized by the Great War, the Russian Civil War, and the Great Patriotic War. All Soviet, and now Russian military planning focuses on preventing such disasters.
The US's primary goal, in contrast, is not homeland security (it is a secondary goal). The US's primary goal is making sure the world's oceans remain open to marine trade. That is why the USSR didn't invest in aircraft carriers, but the US did.