It's not pre-combustion vs. direct injection. One of the noisiest diesels ever made was the mid '90s Cummins 5.9 with direct injection.
The main reason modern diesels are so quiet is because they have electronic injection, similar to a gas engine, but at much higher pressure. The timing can be adjusted by the computer, but most importantly, the system allows multiple injection events, per power stroke. So, at idle, the computer will inject a very small amount that cannot make much noise, then add several more shots to continue the burn. The injectors are simply "on" or "off" and are always supplied with high pressure fuel. With mechanical injection, the entire amount to be injected is done in one shot and causes a very abrupt and powerful pressure rise. A "knock". Also, if either system is not clattering as much as expected, it probably meas the timing is retarded for emissions. And that probably means it is running less efficiently than it might. Possibly cleaner, but at the cost of using more fuel. Diluting the air charge with exhaust, EGR, also slows and cools the burn, which may quiet it some too.