What it really comes down to is diet. Oysters are filter feeders, needed large volumes of phytoplankton to keep them alive and healthy. If you have an overabundance of plankton, then oysters will be great filtration. I know of at least one case where arks (which have a similar diet) grew spectacularly in response to an outbreak of green water.
In the aquarium, phytoplankton is usually at very low levels. In most cases, we have to add it to keep filter feeders happy. What we want to get rid of in marine aquaria are dissolved nitrogen (in the form of ammonia and nitrate) and phosphate. Tridacnid clams can take up small amounts, but the normal way to deal with them are live rock, water changes and macroalgae.