Depending on the climate, you will need a steel reinforced concrete slab, a mortar bed, and then grouting ffor the wet laid. That is more work, more material, more skill involved, no forgiveness, and much closer to permanent. Any problems or flaws are much more expensive to fix.
Dry laid is flexible with freeze thaw, less permanent, easy to fix, costs less in materials, and requires less diversity of experience and knowledge.
Wet laid is much better around swimming pools where bare feet pick up sand and are more likely to catch an edge that are not smoothed by grouting. Concrete paver guys will probably take issue with that, but that is my opinion.
It also depends on the material you are using as well as how you are using the patio. Dry laid irregular stone with big joints is going to be a problem if you have lots of ladies in spike heels hanging at the mansion. It is great if you want planting pockets and have people in more casual footwear.
It comes down to the paving material, surrounding activities, who is going to use the space, how the space is likely to be used, skill and experience level of the installer, aesthetic taste, and budget. Good design will account for all of these things and they will be weighted accordingly.