One thing is that there's almost no difference in price (both tests against leak test only). Another thing is that is must be good for something as soon as most of the tool manufactures in the automotive industry sell diesel comp testers (adapters and gauges). By the way, it doesn't matter if it's an aspirated or a turbo diesel, they perform exactly the same at those testing rev speeds.
The comp test on a diesel engine is good for is that tells you something about the difference in compression between the cylinders. It doesn't help to find out if the piston rings are worn as opposite to the petrol engine ('cause you can't pour oil in the cyl) though.
In this case, presuming one cylinder is leaking because the piston is cracked, you'll know a little bit more about the other three. If all 3 will show about the same pressure, with less than 30-40 psi (or 50-75 psi, depending on the engine size and comp ratio) difference between them, they are ok, you'll only need to replace a piston and it's rings. If too much difference between cylinders you might consider scraping the whole engine or replacing all rings, reseat the valves, ... it depends on what you find on the leak test.
The idea is to take both of the results into consideration.