It's usually color that grabs me first, and sometimes it grabs me in a bad way. If the colors clash or the overall look is just weird (to me) I don't try to analyze it any further, just kind of turn away mentally.
If the color is exciting, interesting or soothing, then I give a second look, and take in the pattern, quilting, and the general feel of the quilt. I would only notice the binding if it stood out in some way.