We actually don't know a lot about this, unfortunately, due to a lack of archaeological evidence. We only have one well-preserved cog (the Bremen cog pictured here, although a more recent find is still being conserved). Studies of the Bremen cog suggest it could carry between 90 and 120 tons of cargo (in modern weight -- not to be confused with tuns, which are a measure of volume). But we know that cogs could vary in size and capacity.

For the Norse ships, we are similarly devoid of much evidence -- the only example of the cargo ship the Norse used (a knarr, not a longship) is the Skuldelev 1 wreck, of which only about 60 percent survives. An average knarr, assuming such exists, might carry 20-24 tons of cargo.

This is a very general question and as such has many possible answers. The medieval ages has distinct periods, distinct construction differences and geographic and political issues which could possibly affect the size of a state's shipping.

Some states did not even have shipping capacities in the same way the dutch or the hanse did.

I would recommend that you start your reading with the excellent phd thesis The Development of a Bottom Based Shipbuilding Tradition in Northwestern Europe and the New World by Hocker.

You can find a free copy in pdf form to read here http://nautarch.tamu.edu/Theses/pdf-files/Hocker-PhD1991.pdf

His bibliography will also help you go deeper into your research if you choose to do so.