I used the Beall System (3 wheels and 3 compounds) for years. I "graduated" to the Don Pencil buff and his PL compound, and haven't used the tripoli or white diamond since. I use buffing to finish my finishes, not to polish unfinished wood. I still use the wax and wax wheel and have never had a problem with it....but typically I put Renaissance over the carnuba so maybe that is why. Tripoli is just coarse enough that it would occasionally burn through a finish...and the buffing wheel needed to be cleaned (raked) before every use. Pencil's PL compound is faster, easier, and gentler, and I've never burned a finish with it.
I've also used rottenstone, pumice, a variety of "deluxing" (rubbing) compounds, automotive polishes, toothpaste, baking soda, and etc., and each will do something to modify a finish. It's fun to try different things, and you never know when your experience will give you that special look for that special piece of work.