Hey there AtheGre,
Example: I've heard Vanderbilt doesn't even really let rotating students scrub, so that could be the most boring/lamest month I could imaging. Other places, like where I rotated truly use the students as part of the team and you really get to do quite a bit.
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Vanderbilt definitely lets visiting students scrub. There are generally 4 visiting students each month between June and September/October. Sometimes there are more. Each student spends 1 week on 4 different services and spends most of their time in the OR (scrubbed).
I will say that standing out at larger programs can be more difficult. If a program gets between 20 and 30 visiting students each year, it can be tough to shine. Also, only a handful of those visiting students will get an interview.
If you choose to do an away rotation, pick a program that you are interested in that is in an area of the country that you might want to live in for 5 years. Work incredibly hard, keep your whitecoat/bag filled with supplies, put gloves on as soon as you enter a patients room and be ready to help, get along great with the residents without acting like you're already one of them, and try not to leave anyone with a bad impression. This stuff might seem like common sense, but you'd be amazed by the number of students that spend the time, money, and effort to do an away and then stand in the hallway while the residents round, don't have a light or tongue blade, etc, etc....
After asking a million people about away rotations as a med student, I decided not to do one. Now that I'm a resident, I can see why many people argued against it. For the average student, it hurts more than it helps. If you are a known asset at your home program, then you'll likely do well during an away rotation, but again, it's hard to learn the system at a new place.
The wildcard in this discussion is that excellent applicants don't always get an interview. You could be perfect on paper and in person, but for whatever reason, your application gets passed up and you don't get an interview at a program you're really interested in. You and the program could be perfect for each other, but you don't get an interview, and the love connection can't happen. That is a real concern, and in my mind, is the only reason to do an away rotation.... if you think you'd rather not get an interview after doing an away rotation at a program than risk not getting an interview having never done an away there, then by all means, do the away rotation and don't leave things to chance.
In the end, its up to you. At my program, there are 1-2 visiting students every year that we would love to take, another 1-2 that might get an interview but not necessarily be ranked very highly, and then the other 80% aren't even offered an interview (as we know, spots are limited).
Best of luck with whatever you decide.