I think it would be harder to police such a world. I mean, alcoholics are loud, anyone who's been around them would know (and who hasn't, I mean, we were all at at least one speakeasy when young, even if we didn't drink there), and they tend to get moreso the more they drink. The amount of speakeasy's that have been busted because the police have seen alcoholics in the street outside, puking thier guts up or fighting (and even more would have been if the mob didn't have such pull with the cops). A world with illegal cannabis is going to be hard to police. Aside from the proven long-term effects, a stoned person is not too easy to spot.
I would imagine that this timeline would still need to have sterner laws against drink than we have against smoke. I would say that being drunk and disorderly on the streets would still be illegal, as would drink driving (I can never understand hardcore prohibitionists who think that legalising it would lead to everyone suddenly taking to the road drunk and crashing thier car into things, there are no anti-prohibitinists who think drink-driving is a good idea).