After about 80 hours (according to Steam) I’m finally done with the trilogy! The final verdict: quite entertaining, if slightly weird (in a good way).
I think quality wise there isn’t much difference between the three parts. I had the impression that the third part was a bit buggy in places, where certain events would not trigger during investigation unless I reloaded the game (on two different occasions). Though that one did do a good job with the cases and the overarching story.
My favorite quote is from part 2, though:
There are quite a number of funny and sometimes unflattering thoughts Phoenix has about various characters. The writing overall is pretty good, actually.
I would certainly play other entries in the series, provided they’ll eventually make their way onto the PC.