Sorry, I should clarify. I do primarily aikido & jujitsu (but I've done TKD, karate before so I know what you are talking about).
There are no stances as such. Remember that stances are simply transitory postures, i.e. you move into a stance to momentarily maintain stability or obtain postitional advantage, before moving again.
Certainly none used in squaring-off or self-defense situations. Even in practice sparring, we never adopt a stance. The only time a "stance" appears is during the "kake" (execution) of the technique.
Every stance has its weakness. Remember the draw a line joining your toes on each foot and bisecting the line in the perpendicular plane?
In all honesty, it doesn't matter whether you're side-facing or front-facing your attacker, but the depth of your stance does. A deeper stance sacrifices mobility for stability. A higher, more natural stance provides mobility (which is what you want in a SD situation).