Interesting topic, Julien.
In my experience, and on our less than perfectly rigid machines, the primary difference between climb and normal cutting seems to be the deflection that occurs, and the ramifications to the size of the part.
The bit will deflect opposite the direction it is spinning into the material.
Often when cutting mating pieces, reversing the cutting direction is all that is needed for a very nice fit.
I’ve not noticed a substantial difference in the finish between climb and conventional. However, I work in a lot of plastics which may just not be ideal for judging cut quality.