The hardness of the metal (or plastic) to be finished is a critical factor in determining the ultimate surface finish in a tumbling or blasting process. Harder metals (steel, titanium, etc.) will typically require more aggressive media to remove burrs off an edge or machine marks on a surface. These types of metals are also much easier to polish and have a greater opportunity to finish close to a near mirror finish.
Softer metals (aluminum, copper, etc.) can be finished with the same aggressive media but the surface finish will be rougher and the edges will be more rounded. It is also much more difficult to get a high polish on soft metals without some amount of hand polishing.
While it is desirable from a operational standpoint to use one media for every part or process, efficiency, productivity and quality can be improved with changes of media. Sometimes just a minor change in procedure may be all it takes.