Just some thoughts:
Graduated filters are better in the square/rectangle variety because that allows you to adjust where the graduation happens, instead of forcing it in the middle of the composition.
All others are generally better as screw on filters because there's less chance of light leaks around the sides that can cause reflections, flaring, etc. You can also usually use your normal lens hood with them, unless they're over-sized and stepped up with adapter rings.
However, I say generally because depending on the lens and filter and focal length, screw on filters can sometimes cause vignetting, especially if you start stacking them, whereas larger-than-the-lens square and rectangle filters almost never do, unless the ring/adapter causes it. There's also that lens hood issue, but that's always true for the square filters which prevent you from using your normal hoods, though those manufacturers make solutions, or you can DIY something up fairly easily.
I have both, and use one system or the other depending on the circumstances.