While I'd like to give my honest opinion about this, I'd just like to preface it by saying that this is quite a politically charged question, which will give you a wide variety of responses according to each person's own predilections and ideological orientation.

Shortly after the October Revolution, in 1918 Rosa Luxemburg prophetically wrote:

Decree, dictatorial force of the factory overseer, draconian penalties, rule by terror – all these things are but palliatives. The only way to a rebirth is the school of public life itself, the most unlimited, the broadest democracy and public opinion. It is rule by terror which demoralizes.

When all this is eliminated, what really remains? In place of the representative bodies created by general, popular elections, Lenin and Trotsky have laid down the soviets as the only true representation of political life in the land as a whole, life in the soviets must also become more and more crippled. Without general elections, without unrestricted freedom of press and assembly, without a free struggle of opinion, life dies out in every public institution, becomes a mere semblance of life, in which only the bureaucracy remains as the active element. Public life gradually falls asleep, a few dozen party leaders of inexhaustible energy and boundless experience direct and rule. Among them, in reality only a dozen outstanding heads do the leading and an elite of the working class is invited from time to time to meetings where they are to applaud the speeches of the leaders, and to approve proposed resolutions unanimously – at bottom, then, a clique affair – a dictatorship, to be sure, not the dictatorship of the proletariat but only the dictatorship of a handful of politicians, that is a dictatorship in the bourgeois sense, in the sense of the rule of the Jacobins (the postponement of the Soviet Congress from three-month periods to six-month periods!) Yes, we can go even further: such conditions must inevitably cause a brutalization of public life: attempted assassinations, shooting of hostages, etc. (Luxemburg, The Russian Revolution, italics my own.)

In short, just a year after the October Revolution, Rosa Luxemburg pretty much predicted the legacy of Stalinism in Communist countries: a politics dominated by single-party rule, resulting in oligarchy and the perpetuation of political terror.

It is fair to say that the Bolsheviks had introduced the strictly centralized, dictatorial rule that reached its height under Stalin. Indeed, under Lenin's chairmanship, the Communist Party continually prorogued the Constituent Assembly and the Soviet Congress, delayed elections, and curtailed democratic rights such as free speech. They were interested in installing the dictatorship of the proletariat but, as Luxemburg argues, this may perhaps better be conceived as the dictatorship of the party.

There are certainly considerable differences between Lenin and Stalin. For example, Lenin insisted on the collective rule of the party. But under Stalin the rule of the party was transformed into the totalitarian rule of one man. I don't wish to dwell on the totalitarian nature of Stalinism, which obviously brought the degree of state penetration of individuals' lives to new heights and forever transformed the level of political terror and political control in Communist countries. I just wish to say that the totalitarian features of Stalinism were altogether absent under Lenin. Nevertheless, they did have their antecedent in the early Bolshevik's dismantling of the democratic organs of the state, as well as their use of terror.

However, what should always be stressed about Lenin in comparison to Stalin is Lenin's impeccable ability to compromise. More than anything, he showed flexibility as a leader. During the hard times of the Civil War, he demanded the harsh requisitions and dictatorial line of War Communism. During peace, however, he called for a "tactical retreat" toward market reforms and the loosening of censorship. Above else, he was a pragmatist, but one whose faith in social democracy was unwavering.

Stalin showed none of the flexibility of Lenin. Once he had consolidated power, he solidified the political system to the point of ossification, with the result that after Stalin's death people spoke of the system--unable to rid itself of the Stalinist legacy--as "post-totalitarian." Stalin heightened the level of dictatorship, political terror, and bureaucratic-state control of the economy, all of which burdened European Communist countries for the rest of their existence. By contrast, Lenin's legacy showed a willingness to adapt and seek the path of reform. Consequently, many reform Communists such as Alexander Dubcek and Mikhail Gorbachev hearkened back to Lenin to legitimate their attempts to reform and humanize Communism. Ultimately, the answer to whether Stalin continued or betrayed the legacy of Lenin is more complicated than it at first seems. Both adhered to the idea of a party dictatorship, although admittedly Stalin opted more for single rather than collective rule. However, I think it is safe to say that Stalin's dogmatic leadership undermined both the original contents of Bolshevik ideology and its original insistence on reform and advancement.

EDIT: Some sources I draw on:

Djilas, Milovan. Conversations with Stalin.

Havel, Vaclav. The Power of the Powerless.

Luxemburg, Rosa. The Russian Revolution. Available at https://www.marxists.org/archive/luxemburg /1918/russian-revolution/.

Steinberg, Mark. Voices of Revolution, 1917.

A book (although I do not particularly like it) that overviews 20th Century Russian history is: Service, Robert. A History of Twentieth-Century Russia.