There are many ways to test the catalyst, but they depend on what you suspect the cat is doing wrong. They all require either tooling or experience to evaluate properly.
A simple test to see if a cat is plugged can be done with a vacuum gauge. Much is subjective but basically the vacuum at idle should go up when the engine is ran at higher rpm UNLOADED. In other words if you raise the rpms to 2000 from idle speed the vacuum should be greater. If the cat is plugged the vacuum will be less.
The problem is that a cat looses its effectiveness long before it plugs. The degree of restriction causes performance problems and the worse it is the easier to find using the above method.
The ability to actually clean the exhaust can be tested by an exhaust gas analyzer and is what most emissions testing does. If you read the gasses before and after the cat the true efficiency is gained.
A simpler less exact method for gauging the cats effectiveness would be with an infra red temp probe (like used for tires). The cat should be hotter at the exhaust end than the intake end while the engine is running (with the cat fully heated).
The factory cats are enormously expensive (probably over $1500), aftermarket are usually less than $500 and are probably not a great deal as their abilities (both immediately and down the road) are worse than 3 to 1. They probably weigh less than a third and are obvoiusly less shielded and smaller in stature. But they can get a car passed. Its a shame that used cats are illegal as I would much prefer a used MB cat to any aftermarket I have seen.
Bosch Master, ASE Master, L1
33 years MB technician