The end result is almost the same between the two. I assume that by distillation, you are referring to steam
distillation. I don't know of another method.
Here is what the idea is: Steam distillation is the process by which water is heated to the point of making steam. The steam rises to a point that is cooler, where it turns back into water. Since its steam, only the water and none of the contaminants rise and travel down to the collection area. Simple_chem_distillation.JPG
In Reverse Osmosis/DeIonization the water is passed through a series of filters, than a type of membrane, than another filter to remove remaiming ions. In a nutshell, the membrane allows water to pass through while other particulates (too large to pass through the mambrane) stay behind. It's the same theory we studied in Earth Science in high school. reverse-osmosis-3.jpg
The general rule is that it is less expensive and more time efficient to do RO/Di. Imagine having to steam water every time you needed water. You would be steaming hundreds of gallons a month!
Are you using Wal-Mart water? I used this for a few years and had no problems with it. I used both the Reverse Osmosis water (drinking water) and the Steam Distillation water (distilled water). Never had a problem with either.