The first obvious affect detuning has is to lessen tension in the strings. This isn't necessarily bad as part of contemporary sonic aesthetic is the strings rattling against frets. One of the down sides is that upper transients are lost. This results in a more pronounced fundamental and a less articulate overall sound. This is problematic as more than half of a percieved note is harmonic content and not merely the fundamental note. Additionally, sustained notes have a tendency to drop in pitch from the time they are struck or plucked until they resolve and fade. The duration of sustained notes is also compromised.
If proper tension, sustain and pitch are desired there are two fundamental solutions; thicker string gauges or a longer scaled instrument. Here are more details on why Size Matters.
Alternate string gauges is by far the simplest and least expensive way to detune your instrument and maintain its proper playability. The lower the fundamental note is dropped below traditional tuning the thicker the string gauge should be. Something to be aware of, however, is that thicker strings reproduce fewer upper transients. They will be a tremendous improvement over detuned thinner strings, but the notes won't be as articulate as they could be. Additionally thicker strings also require a longer scale length and may not be able to be intonated properly.
String guage alternatives will be found here in short order. The list is expected to be short and meant to be a starting point for your own experimentation. As with any instrument choices of this sort are personal so please bear this in mind. Feedback on the recommendations is welcome. Email me with suggestions for information you would like to see addressed on this topic.
Ultimately the best way to get superior tone from a detuned or drop tuned instrument is to use an extended scale length. Where guitars are concerned, baritone instruments are commercially available that will allow a natural detuning of as much as three half tones. There are a variety of scale lengths to choose from.
Bassists have options as well though they aren't as plentiful. In general bassists must consider both increasing string gauges and making use of extended scale instruments to drop their fundamental a whole step or more.
The longer the scale length of the instrument the thinner the strings can be, and the greater tonal range the strings will produce.