[tarentel]

Lenin, and probably others, advocated for the use of a state to transition, not Marx. The dictatorship of the proletariate is a transitional period when the proletariates take over the means of production through revolution. There are still classes at this point, hence transition, but the ruling class is the working class. In other words, a "dictatorship" of the many and not the few.

As far as the split goes, it was a lot more involved than just one issue. The problem you are referring to, however, had more to do with using politics of the time in order to motivate workers which they both understood in many parts of Europe were not ready for what they wanted. Marxist were ok with participating in politics, Bakunin was not. They both agreed though that real change would come from an uprising of people and not through political action.