Driven wells are common in our area due to the extensive lacustrine unconfined aquifer under our area of NY. I use a New York DEC online well drilling database
that documents wells driven since the program was instituted. Between Greene & Ulster Counties I think
they list something like 1,000 records and scrolling through I saw only a handful of very shallow wells that I categorize as less than 30 foot. I include a screenshot of the only well less than 20 foot which could well be a typo, but this gives you a idea of the data provided. The link on the table under “registration number” provides the name and contact info of the company that drilled the well.
So looking at that I would say that drilled wells are far more common in your area of the Catskills versus my area in the lower Adirondacks due to the local
geology. What is better between the two methods is contingent on what they find when they drill, informed by knowledge of the geology and past results nearby, but even that doesn’t guarantee good water at any anticipated depth as two wells 100 yards apart can provide very different results.
The other obvious issue with shallow wells is the concern about surface pollution finding its way to the water table whether it be improperly maintained septic or agricultural pollution, hence many localities no longer allow shallow wells because of these problems. Our point is at 25 foot and provides something like 10 GPM (there is a 100 foot well nearby that provides over 100 GPM from this underground
sand aquifer). If I lived on a small lot with nearby neighbors and septic I would be reticent relying on a shallow well depending on the details.