Since it will be more on semanthics... Since yes I can agree that the cooling solution of X1X (and possibly X1) were stronger and quieter (but don't know about the power drain or cost) we can certainly say it is more effective or stronger, efficiency is something we can't directly calculate. Anyway as you said both done the job and certainly since a very good portion of gamers consider the noise a relevant point (I don't, while playing it never bothered me, although my fat PS4 is quite noisy even on home when my son is using - possibly needing some cleaning and perhaps thermal paste replacement) I can concede that the cooling solution on Xbox was superior this gen (and well it is possible to be superior on next gen since we already know XSX is improved over the X1X and PS5 even though said is improved we don't know how much, and well it would take a major improvement to get close to XSX).
What makes it superior though?
Speaking on function, yes, it was quieter, but it was also bigger and later on, a more expensive solution. These are both things that sony could just as easily have also done,it doesn't require any kinda engineering genius to in one case say "ok, make the case bigger and put in the biggest fin array and fan we can fit into it" and in another case to say "make the case smaller and put in a vapor chamber cooling solution".
In case A, bigger case,bigger fins,bigger fan + lower RPMs + more air volume = quieter operation. In case B, vapor chamber cooling = more expensive but faster thermal dissipation. These things ar all deterministic, ad very common. Its clear sony went a different route, and one mostly determined by staying withing a particular form and pricing factor. But at the end of the day, their cooling solution did what it was designed to do, cool the system and keep it running. If it had a RROD level thermal failure type thing then we could say it was poorly designed or bad.
This is like saying a 500HP V8 (usually between 4-6 litre engine) is better designed than a 500HP turbocharged 3.0 litre engine that has similar performance because the V8 sounds different.