From an economic point of view, there are both similarities and differences between these two.
The two cases are both similar because they both involved total prohibition of the products in question. In other words, these were not instances in which the government regulated a market. Instead, the government simply shut down the official market for each product, forcing them to be sold on a black market.
The major difference between the two has less to do with the laws themselves and more to do with the public reaction to those laws. Economically speaking, there was a great deal more demand for illegal alcohol during Prohibition than there is for illegal drugs today. This led to a situation in which breaking the law was much more lucrative for a larger number of people than it is to break drug laws today. From an economic point of view, there was more incentive for suppliers to supply illegal alcohol than there is for them to supply illegal drugs today.