Reverse Osmosis is a process/technology that uses a semi-permiable membrane. The purity of the water really depends on the membrane used, concentration of "impurities", pressure & water flux rate.
Distillation is another liquid purification process that involves boiling the liquid then condensing the steam into a "clean" containment unit. Some trace elements are still left after the distillation process.
All in all RO water if done right with accurate precision is better (in terms of purity)than distilled water. However the cost will out weight effectiveness greatly. (if you are local we did learn this in our early secondary education)
Invest in a TDS(Total Dissolved Solid) meter so you can test on the quality of the processed water be it is done by RO or distillation.