distilled watter is more pure. It has nothing in it at all. It will keep your creedo/beads/oasis/whatever clean.
it also has no ordor or taste. A few months ago the Akron water supply had a HUGE alge problem. THis caused all the water in akron to smell very bad. If this water would have been used in a humidor it would have made the humidor smell bad and the cigars would pick up this taste also.
Tap water is a sure fire way to ruin not only your humidification device but your humi too. Tap water (as Matt said) contains all kinds of stuff that will eventually clog the poors in the grain of the wood and keep it from absorbing and releasing humidity.