As an Elementalist, my primary source of both Stability and stun-breaks is [Armor of Earth]. As this is the only class that I play, I feel I have some misconceptions about what Stability is and what a stun-break is.
So far, I believe that Stability is capable of preventing Immobilization. However, stun-breaks cannot remove Immobilization. This leads me to believe that there may be more differences in the the capabilities and usage of Stability and stun-breaks.
What kind of differences are there between Stability and stun-break? When is it best to use either and what kinds of things are they vulnerable to?