There is an enormous choice of underlays to use with your carpet. Not only the difference in construction, but also a choice of either wool, hair, wool/rubber mix, rubber or foam to name but a few!
It is widely regarded that felt is the best choice. With respect to wear, not only of the carpet, but also of the underlay itself.
Choosing an underlay has much to do with the recommendations of the carpet supplier.
Some manufacturers will not recommend anything other than a good quality felt i.e. wool or hair waste.
While others are biased towards certain brands.
With everything, there is the question of cost. At the cheaper end, choose from foam underlays, cheaper because
of the materials used. Being synthetic, they are more available, and less costly to produce.
Mid range, the quality rubber underlays are a better option, but are more expensive than foam.
With the rubber underlay it doesn't tend to break up as easily, which leads us to felt.