Are there an advantages of doing courses in pure maths (master level) courses, if you want to apply to physics grad school for a phd in areas such as string theory, or high energy physics? Apart from the obvious advantage, that you get better at math, which is used a lot in this areas, I am asking about the direct advantage for grad school applications on the transcript? Does the selection committee like to see more grad level physics courses in maybe slightly irrelevant areas, or pure maths courses which have use in these areas?
I think the real answer is that it depends on what it is that you're planning to do. The more closely your courses align with your proposed field of study, the easier it is for the committee to evaluate. So, taking pure mathematics courses makes more sense if you're going into a theory-based field than if you're doing something more experimental in focus.
However, you should also keep in mind that a strong grade in an upper-level mathematics course will at best be "neutral," and it might be possible to explain away a bad grade; a bad grade in any physics course will not go over so well. So you should factor your interest level and ability to handle the courses in your selection process. You should also consider if the course in physics is considered a "standard" course for undergraduates pursuing graduate admissions. If so, then it makes more sense to take that class than an elective mathematics course. (Otherwise, the question will of course be "Why didn't you take course X?")