This paper presents the results of an empirical study and a real-world deployment of a gaze-adaptive UI for Augmented Reality (AR). AR introduces an attention dilemma between focusing on the reality vs. on AR content. Past work suggested eye gaze as a technique to open information interfaces, however there is only little empirical work. We present an empirical study comparing gaze-adaptive to an always-on interface in tasks that vary focus between reality and virtual content. Across tasks, we find most participants prefer the gaze-adaptive UI and find it less distracting. When focusing on reality, the gaze UI is faster, perceived as easier and more intuitive. When focusing on virtual content, always-on is faster but user preferences are split. We conclude with the design and deployment of an interactive application in a public museum, demonstrating the promising potential in the real world.