There are two obvious differences between prohibition of the two substances.

The first is that cannabis use was never as embedded in society in the United States (and Canada and European countries) in the way alcohol was. Alcohol use has probably been standard for people across all social classes in these societies since their origins.

Cannabis, on the other hand was prohibited as it was becoming popular in the US (partly as a result of the prohibition of alcohol). Moreover, its consumption was associated with lower classes, particularly Mexican immigrants, and was not widely used among the middle or upper class.

The second big difference is that the classification of cannabis as a harmful, illicit drug has been widely accepted by other countries. This was not the case with the prohibition of cannabis. If the US was unusual in its prohibition of marijuana people's attitudes towards it would inevitably be differ. In addition, the easy availability of alcohol in other countries would have made it a lot easier to smuggle in.

The most obvious similarity between the two prohibitions: they are both highly ineffective. The prohibition of marijuana has not stopped its use being widespread, and tougher law enforcement has not led to a significant reduction. Indeed, there is good evidence that relaxing laws can reduce consumption. (Consumption in the UK certainly went down after it was downgraded from class B to C - but that's strictly off the record since it happened less than 20 years ago so it's not officially history.)

Main source: The Pursuit of Oblivion: A Social History of Drugs

(edit: slight tweak for sense.)

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