I think both should be effective against each other.
If you throw poison in a glass full of water and give to someone drink, they will get poisoned.
But if a poisoned person drinks lots of water, the poison may fade way of their body (I have read this somewhere, but I am not really sure).
Anyway, making Poison SE against Water would make the type way more useful...
I like some Pokémon of this type, but it is quite pointless to use them in-game, since their offensive capabilities are poor.