An away rotation lets a program get to know you much better, and vice versa. As you probably already know, it's sometimes hard to shine during the med student rotation. Since you aren't given many responsibilities it can be hard to demonstrate how good you are, and a program might think you're mediocre. But if you make a concerted effort to get to know some faculty, you'll probably succeed.
In any case, if you're going to do an away rotation at a place you really like, then try to first complete an anesthesia rotation somewhere else to build your knowledge base and confidence.
Another important consideration is that you'll see all of a program's moles and blemishes if you do a rotation there. I met a lot of applicants on the interview trail who no longer liked program X or program Y after doing an away elective and planned to rank those programs pretty low.