<p>I am sure that someone more knowledgeable in engineering will correct me but I think a good analogy would be that Applied Mechanics is to Mechanical Engineering as theoretical physics is to experimental physics.</p>
<p>As for a choice between physics and applied mechanics. It is really a question of whether you prefer engineering or science. There are a lot of things in common but the fundamental motivation for the field is different. As a physicist, I don’t think that physics is any more prestigious than engineering as for popularity, I think that more students want engineering than physics.</p>