Drilled wells are better than a dug well as drilled wells can reach deeper sources of groundwater which means that the water is less likely to be contaminated and it's less likely that the well would dry up in a drought.
Dug wells are okay but they are prone to drying up from drought if you don't get enough rain or precipitation and they are at higher risk of becoming contaminated.
When you drill a well you can drill to 100 feet or more and reach cleaner water and in most cases the deeper you drill the less chance you have of it drying out as there is usually more water the deeper you go.
My well is 150 feet deep and we get a lot of rain here and so it's very unlikely that the drilled well would go dry.
Even here I can dig down 2 feet and water fills the hole although it's dirty water.
So since our water table is at 2 feet down it means that my drilled well is unlikely to go dry anytime soon and we get plenty of rain.
I have had a dug well in other dryer locations and they went dry when he didn't get enough rain.
But my drilled well has never gone dry and unlikely would and I could probably get millions of gallons out of it a day if I had a pump that big that could draw that amount of water and it still would likely not go dry.
Wells that are for households and for drinking water should ideally be at least 100 feet or more and some locations you have to drill to 200 to 300 feet or even deeper to reach any water depending on how far down the water table is in your location.
Places that get a lot of rain and precipitation have a higher water table and you don't have to dig as deep but in dryer locations without enough rain or precipitation you usually have to drill down deeper to reach any water.