Ok, here a dystopic question: Considering that against all odds, Beria becomes the leader of the Soviet Union, how would such state look like, and how it would develop different from the Kruschevist Soviet Union?
First of all, one condition I want to stabilish is that Beria is prepared for Stalin's death, let's not go for the conspiracy theories that he killed stalin or anything, but on this scenario he knows for a while that Stalin might be dead soon, and this allows him to pull enought resources, man and planning in taking over the State, and so at the death of Stalin he manages to use his huge wibe to overmanouver his enemies and take over the government, also purging Kruschev, Malenkov and others.
Another point is that this Beria holds the power until the end of his "sane" life, or to put more simple, he was born in 1899, let's say that he can commands the government before his capacity to lead gets seriously crippled on the mid-late 1970s, that means that we have a NKVD state that will last from 1953 until somewhere on the 70s. What are the butterflies on the cold war, and does this Soviet Union endures longer or less time than the OTL soviet union?
Strictly speaking, it would not be "NKVD state" because NKVD ceased to exist in 1946 (and Beria lost his position) being replaced by the Ministry of Internal Affairs (MVD) which Beria (when reappointed as head of the MVD) merged with the Ministry of State Security (MGB). The merge continued from mid-March 1953 until mid-March 1954 after which these agencies were separated and MGB "demoted" to a committee status (KGB). So how about the "MVD state"?
As for the rest, it is a wild guess but it probably make sense to consider the following factors:
1st, the people who did end on the top in OTL also had been heavily involved in the atrocities of Stalin's regime, GULAG was not abolished until 1955 and KGB remained a powerful organization almost until the very end of the SU even if the methods changed (Andropov used involuntary commitments to psychiatric hospitals, deportations and arrests of the activists to achieve "the destruction of dissent in all its forms") . We can only guess how things would develop under your scenario.
2nd, during his life time Beria was regularly in charge of the areas related to the technological development (nuclear program being one of them) and at least had some idea about the Soviet economy while Khruschev was a pure "apparatchik" with no clue. As a result, when in power Nikita was steadily marching from one disastrous decision to another. It is possible to assume that some of these disasters could be avoided by someone more experienced (an argument seemingly popular among Beria's apologists) but OTOH it is rather hard to tell which methods Beria in power would be using.
3rd, it seems that Beria was willing to at least consider unification of Germany on conditions of getting a big Western help (which would be definitely good for the Soviet economy), which could result in an early end of the Cold War and numerous butterflies in more than one area.