Many people would consider these two leaders very similar, but some key philosophical and functional differences existed between the two.
As for the similarities, they both wanted to transform Russia and, in turn, spread that transformation throughout the world. They were both members of the Communist Party and used the power of the government to enact social and political change. Additionally, both spent time in exile before the Bolshevik Revolution.
In terms of differences, life was probably better under Lenin than Stalin, but that would depend on the point of view of the individual living there. Lenin wanted to use communism to free the working class from exploitation at the hands of Russia’s elites. His promises of Peace, Land, and Bread were praised throughout the land. His goal of creating a classless society typically raised the standards of living for most proletariats. With that being said, Lenin was responsible for many executions, censorship, and atrocities at the hands of his secret service, The Cheka.
Stalin thought of communism as more of a means to institute totalitarian control and maintain power than Lenin's more utopian view of the new government. Stalin was much more brutal than Lenin, with some estimates claiming that up to twenty million citizens died under his command. His major objective was to turn Russia into a modern industrial society and he collectivized all agriculture taking away the limited land ownership allowed by Lenin. Individual freedoms were curtailed, education was strictly controlled by the state, and people lived in fear of their neighbors "informing" on them which resulted in severe punishment that was often based on little or no facts.