Both helix derivative and low-cut filters can be used to enhance the details of images. But which one is better? It depends on the situation.
Both helix derivative and low-cut filters cut off the zero-frequency component, but the functions of the frequency are different. The derivative filter's response is approximately a linear function of frequency, while the low-cut filter's response has a hole below the cut-off frequency and is flat above it. This leads to the main difference between derivative and low-cut filters: the derivative filter enhances the small-scale structures more, while the low-cut filter makes medium-scale structure much clearer.
In Figure 2, a long line structure in the middle of the sea is very clear in the plot created by operator; in the plot created by helix derivative filter, it is too weak to be seen. The helix low-cut filter preserves this structure quite well, as shown in Figure 7.
Another difference is the cost of image processing:
So if the main interests are the small-scale structures or the high costs of computation are not affordable, I should choose the helix derivative filter. Otherwise, the helix low-cut filter is a better choice.