There are three (3) basic types of rims (hoops) : Die Cast, rolled & wood.
Most drums come will standard rolled rims. As a general rule, the die cast and the wood are reserved for snare drums, normally as an after market change.
The die cast as more solid than the standard rolled so they are thought to hold a tune better and provide a more aggresive sound for both cross sticking and rim shots The wood rims can provide a very nice cross stick, but I have not found them to be significantly better than rolled for rim shots. I have not seen or heard any specific advantage with wood rims related to holding a tune.
I have not really noticed any other specific inpact on the tone of the drum in general when comparing these three styles of rims.
