Note: there is a lot of misinformation to disentangle in this question and the topic of Russian peasant agriculture is a massive one in the relevant historiography and the experience of a Russian peasant farm is going to differ quite widely in say, the Black Earth belt compared to the Western Provinces, so I'm painting with a broad brush.

Despite the impression that the Russian commune (obshchina/ mir) was a timeless institution, the reality was the commune was an institution in a state of flux. Narrowing the scope down a bit, the Great Reforms of Emperor Alexander III simultaneously both reified and undermined the commune as a Russian institution in the countryside. Emancipation was a mediated process and the elders of the mir were responsible for remittances to the former landlords for emancipation of the serfs and controlled the social life and patterns of the commune. Additionally, the commune elders were responsible for controlling the movement of the peasants and they could not leave the commune without permission of the mir's leadership. The nineteenth-century commune held the land in common and divided out how it was to be partitioned out for each harvest. State imperatives to control the peasant masses dovetailed with the elders' desire to strengthen various families' local power. This made the commune a very socially conservative institution that was resistant to innovation and change. Most commune leaders were reluctant to innovate with new agricultural techniques and those peasants who became lucky enough to buy their own land from the commune and own their own farm became social outcasts.

But the mir became a symbol for a simpler life and its communal living an antidote to modernity in prerevolutionary Russian culture. Russian literati like Tolstoy celebrated the peasantry's communal culture for its honest sobriety and clean living. Other political dissidents and intellectuals saw the peasantry as a latent mass for revolutionary change whose collective way of life opened up an alternative route to utopian reform.

however, just as the communal system was being celebrated by a generation of intellectuals, the Russian state began to see the peasant commune as a problem. Both the development-minded Sergei Witte and Stolypin saw the persistent underperfomance of Russian peasant agriculture as a problem to be solved. The Russian Revolution of 1905 provided enough of a shock to the existing political system to enable a wider reform of agriculture under Stolypin. The agrarian reforms of 1910 allowed communes to self-dissolve and partition the land out into private plots and provided for institutions like the Peasant Land Bank that provided loans for the peasantry to improve their land with new equipment and machinery. Stolypin termed these reforms "a wager on the strong and sober," and hedged his bets that a conservative peasant culture, if freed from the sclerotic obschina would become a bulwark against revolution and support the tsar.

While some peasants did avail themselves of Stolypin's reforms, they were not popular with the conservative Third Duma and the Tsar and Stolypin had to fight an uphill battle to get them passed. Therefore, the situation of Russian agriculture in 1914 was rather mixed, with some communes still existing and other peasants availing themselves of Stolypin's reforms. The war though, threw the countryside into disarray. State control of prices threw the rural economy into a freefall and although there was an initial enthusiasm for the war, such sentiments quickly soured. The gradual disintegration of tsarist state authority and legitimacy created a vacuum within the Russian countryside as the tsarist bureaucracy was perennially understaffed. The Revolutions of 1917 provided both a pretext for a massive redistribution of land and the ideals of 1917, which were often quite ill-defined, stoked hopes for a more utopian rural order. Although the "Black Repartitions" in which large landowners estates were seized and partitioned out into a reborn commune, these were not quite the same mirs as those of the Great Reforms. On the surface, the collective ownership of land and its partition seemed like a return to a pre-Stolypin system, but radical politics and other forms of transgressive ideas had also found a role in the new commune, something that the tsarist authorities would have never countenanced.

The Bolsheviks for their part sanctioned the Black Repartitions partly for tactical reasons as it undercut their ideological rivals the SRs, but also because it cut the Gordian knot of the land issue. However, the truce between the countryside and Bolshevik state was somewhat temporary. The Bolshevik leadership feared, quite correctly, that the communal redistribution of land was inherently unproductive and the need to feed the cities skewed the balance of power between urban/countryside to the latter, which was an embarrassment for an avowedly proletarian revolutionary state.

Collective farms (Kolkhoz) and state-owned farms (Sovkohz) were two solutions to this impasse. Sovkohz was the proffered solution as the state owned the land, agricultural tools, and farmers who worked the land were paid a wage for their labor, in effect transforming the Soviet peasant into a rural proletarian. But Sovkohz were expensive and time-consuming, so the Kolkhoz option became the path of least resistance for the state. The Kolkhoz amalgamated the various trip farms into a single plot and pooled rural labor into brigades to work the land. Both these systems had been in operation in various forms since the Civil War, but they were unpopular with the peasantry as they meant abandoning local autonomy of the collective. The Stalin turn forced the peasantry into the Kolkhoz and added more elements of state regulation and control. Although there was some upwards mobility for peasants within the kolkhoz such as moving from laborer to tractor mechanic, the Stalinist government saw instituted yet more elements of regulation tying the peasantry to the collective farm. The rushed nature of collectivization and the tolerance of brutal methods in the name of getting the job done meant that the initial results of collectivization were famine and violence against the purported class enemies of the state.

So pace Wikipedia, the phrase "centuries-old system of farming was destroyed" is one that generates more heat than light. Although there were superficial continuities between the Kolkhoz and the Obschina, these parallels either disappear upon closer examination or have to be significantly modified. For example, the communes' regulation of peasant movement was done for quite different reasons in the nineteenth century than under Stalin, and the punishments for transgressing these limits were much, much more severe under Stalinism. Moreover, the ones in charge of regulating the peasantry were quite different as it was a matter for the police, not the families-run commune. If one could create a composite of a typical Russian peasant (if there is such a thing) of 1883 and plop him down in the peasant world of the 1920s, he would likely be quite confused by things like civil marriages and the dependency of the church on peasant largess, even if he did recognize the role of familial politics in the partition of land.

Sources

Moon, David. The Russian Peasantry, 1600-1930: The World the Peasants Made. London: Longman, 1999.

Nove, Alec. An Economic History of the U.S.S.R. London: Allen Lane, 1992.

Retish, Aaron B. Russia's Peasants in Revolution and Civil War: Citizenship, Identity, and the Creation of the Soviet State, 1914-1922. Cambridge, UK: Cambridge University Press, 2008.

Weeks, Theodore R. Across the Revolutionary Divide: Russia and the USSR, 1861-1945. Chichester, West Sussex: Wiley-Blackwell, 2011.