@DecentLevi
In the end, both cotton and aluminum foil + butyl putty do the same thing just in different ways. Foil+butyl acts as a (solid; closed cell) barrier which is going to provide (mostly) vibrational control dampening, while the cotton is (mostly) doing vibrational absorption by converting vibrational energy into thermal energy by way of friction of air passing through it (similar to a pop filter; breathable, open cell). In both cases, vibrations/reflections are reduced. This matters in the case of treble/soundstage because higher frequencies (generally) lose energy faster than lower ones. Sound imaging is mostly perceived from the higher frequencies, the higher you go the more that affects soundstage (while bass virtually can't be perceive for imaging at all). But that's not a problem, consider the fact that the original recording already has all the reflections of the room (or echoes added in post) that the artist wanted it to have. Having more reflections inside of the earcups messes with the imaging of the original recording. That is why open-backed headphones have more detailed soundstage imaging than closed headphones, they have less reflections since the backing is usually just a grill.
Here's great educational YouTube video to explain the difference between vibration control dampening and vibration absorption:
So, essentially I can't tell you which one will reduce the vibrations/treble more between the cotton and the foil+butyl since I don't have both to test (though I do have a pretty good guess since I've worked with both), but what I can tell you is that they
both will reduce vibrations/treble. The only other thing of concern (other than which one is more effective) would be how much space it takes up inside the headphones (or if it constrains air flow which would effect the bass), how much time/effort is involved, and the cost. I trust you will be able to discern those by yourself though.
One last thing, when using sound/vibration dampening barriers/materials (such as foil+butyl) you have the option of placing (adhering flat against it really) the material either on the inside of the earcup, the driver itself, or both. When placing the material of the driver itself, then that will absorb a lot of the vibrations as they are being produced reducing the treble a great deal and the vibrations that would eventually have reflected off of the earcup later. But with placing the material on just the inside of the earcup you reduce the vibrations (mostly treble) that would have reflected off of the earcups, which means reducing the reflections without reducing the treble too much to cause the soundstage to lose detail as well. The same principle applies to placing a sound/vibration absorption material on top of the driver (say a mesh/cloth or foam filter) rather than placing it on the inside (like the cotton fence). Though out of the four, the sound absorption filter causes the most loss of detail since it is filtering all of the sound right before it is going to enter into your ear.
Best Regards,
Lyova Margaryan of Tru-Fi Speakers