I don't know the difference between a pounded well and a cable tool. They seem to be used interchangeably but I think they may be different.
They are the same, also called driving a well.
But the two major reasons were that a cable tool usually gives you more water because it fractures the rock as it goes through and doesn't use drilling mud. The rotary rigs either use high pressure air or mud and both methods tend to clog the pores in the rock. Also, I was warned by not only the state but by several folks that had rotary rigs drill their wells that the rotary rigs drill so fast that they can shoot right through a water bearing layer and drill deeper to another water bearing layer.
This is my understanding as well. I worked for a drill for a few years, we used a rotary, but towards the end we setup a cable rig to use in some cases. Another advantage of a cable rig is that it has a small footprint so you can wiggle one into areas that you can't get to with a traditional rotary as they are big.
There are downsides to a cable as well. If there is a softer formation on top of a harder formation and the delineation is at a steep angle it will push the bit sideways until the bit can penetrate the hard formation. This creates a dogleg making it difficult/impossible to put the casing in and if left an open bore (no casing) it creates a hazard that can catch a pump / drop pipe causing them to get stuck in the well. Cable rigs suck in hard rock. Your always having to sharpen the bit and it is difficult to trip in and out as you have to screw several lengths of rod to the bit to give it enough weight to break the rock.
There are three major types of drill bits used on rotary rigs. The first two bits use drilling mud to provide lubrication, remove cuttings, and keep the bore open. In normal circulation mud is pumped down the drill stem and circulated up the annular between the stem and the bore wall. Cuttings then fall out in the mud pit before the drill mud is recirculated.
Drag bits are used in soft non consolidated soils such as gravel, and sand. These bits have a fast cutting action and are relatively inexpensive.
www.bluedemon.com
For more consolidated formations such as sand rock, fractured rock and mixed formation a tricone bit is used. They are more complex than a drag bit and therefor cost more to run.
en.wikipedia.org
The third drill bit is a Down The Hole Hammer (DTH). They are air powered and the air exhaust pushes the cuttings out of the hole. It is like a jack hammer that is being spun slowly by the drill rig. Water is used to help cool the bit but because the formation is hard enough to require a DTH it does not require drill mud to apply hydraulic pressure to the bore wall to keep the hole open. This is the most expensive way to drill a well as the bits and hammers are major money.
Center Rock offers the most complete line of dth hammers, drills, and bits which are designed for peak performance in all rock drilling applications.
centerrock.com
Hope this helps.