Please read the whole thread I gave Rick67 on how to care for your distiller, because of what Trapper said about the filters (you don't need them).
Now then, to answer your question, distillation is the only procedure that gets 100% of the fluoride and chlorine out!
Reverse/Osmosis gets out 95-96%.
Both processes will also remove minerals, and why we tout that people should REmineralize their water by adding 1/4 tsp of Seasaltlike this kind into each quart they drink. And if one doesn't like the taste, one can do "salt shots" - get it in in one swallow, and then drink the rest of the quart plain.
A person should drink half their weight in ounces of water daily.