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This is a test of the GoPro 3+ Black in regards as to if it is better to record in 1080 Narrow to get rid of the fish eye, or record at a high resolution and crop later if you need to.
Short answer is 4K Wide Cropped to remove fish eye will not cause any loss of resolution compared to recording at 1080 Narrow, but it's only 15fps.
2.7K Wide can not be cropped to a small enough area and have as good resolution as 1080 Narrow mode.
However, 2.7k Medium can be cropped to 1920x1080 and it will be the same image (or very close) to the 1080 Narrow.
So to sum it up if you think you may want to crop out fish eye from a recording you are going to make, but want some extra width in the recording just in case you can use it, record at 2.7K Medium and you can crop out the fisheye and not lose any resolution compared to 1080 Narrow Mode .