Assuming it is a digital camera, my understanding is the lower the frame rate the less memory is required to store a given length of video. However, a slight choppiness may be observed at the lower frame rate.
Just the opposite for the higher frame rate. The higher the rate, the more storage is required to store the same length of video, however, choppiness should not be observable.
Most video is 30 fps which produces smears where there is fast action. Movie film rates are often 24 fps, which makes it even worse. 60 fps will allow you to capture sharper action shots creating a overall crisper image.
The type of image compression also effects overall quality.