FELT PADS
As the name suggests, made from felt, and it can be of different hardness. Attached to the cups using screws, washers, and bushings. Some like them, some hate them, like everything else
HARD PADS
Usually some kind of hard backing, delrin (Polyoxymethylene), aluminum, or brass, and a soft top layer, usually suede, whether natural or manmade. They also usually come with stabilizers which are glued to the cup. Brands that make variations of this kind of pad are Straubinger, Pisoni, Jim Schmidt, Muramatsu, and Powell in the past. The advantage is that these thin pads don't change much with humidity which can be a problem with felt. Installation requires some fine touch and precise shimming, while felt pads are usually set by using water and sometimes heat.
MAGNETIC PADS
There is a new kind of pad out there installed on Matija flutes only at the moment. The stabilizer is a one sided multipolar magnet, and the pad contains iron powder, whether mixed with silicone or made with iron rubber and suede. The advantage is that there is no distortion due to the compression by screws, washers, and bushings. Installation requires similar skills like hard pads. They are shimmed in the same way. Although the pads are flexible, they behave like they are hard because they adhere to the magnet stabilizers glued to the cups which are of course flat and not flexible.
Which pads are the best?
There are various answers to this depending on who you ask, so we will just go with the fact that whichever pad is used, it should perform well if installed properly and skillfully.