I don't think this is an issue of showing, just a little riding quirk. I also own a horse that stands around on his own with his head high most of the time, and a lot of it has to do with the horse's state of mind. When they are alert, excited, angry, nervous, or scared, they brace their neck and their head goes up.The relaxed frame shown is what your horse is more comfortable in because he is calm, relaxed, and listening to you. It also develops the top line muscles in the neck and back. Strive for this, and you can do well in any discipline-EP, dressage, jumping, you name it. A quick hint: look at the differences in your position of when she has her head high vs when it is relaxed. For example, notice in the high head pictures, the line from her mouth to your arm is broken-you are both bracing together. In the relaxed pictures it is the same line, you are both loose, supple, and synchronized.
"The trouble with the world is that the stupid are certain and the intelligent are full of doubt"