It's difficult to make a general statement about whether EQ shelving or high-pass filtering is "cleaner" or has a more natural sound, as it can depend on the specific situation and the goals of the processing.
However, in general, a low shelf cut may be less disruptive to the overall tonal balance of a sound than a high-pass filter, as it allows the frequencies below the shelf to remain relatively untouched while attenuating the higher frequencies
. This can help to maintain the natural character of the sound while still addressing any issues in the upper frequencies.
High-pass filters, on the other hand, can be more effective at removing unwanted low-frequency content, but can also have a more noticeable impact on the sound's overall tonal balance and may introduce phase issues.
In short, the choice between EQ shelving and high-pass filtering may depend on the specific needs of the mix and the desired outcome.