Compression test

I assume what you call the "differential compression test" is what I call the Cylinder Leak Down test.

In my opinion both diagnostic tests can give valuables information about the health of your engine.

The Leak Down is probably the more valuable/informative of the two.

I’m with Sean. I prefer the  leak down test / differential compression test.

I believe the OP is asking for reasons, not just opinions. I too would like to better understand the reasons.

Exactly, I have the equipment for both and do both.  Knowing the prop is going to turn is better to me than guessing if it going to jerk!  

https://www.motortrend.com/how-to/engine-diagnosis-leakdown-compression-test/