The actual sleeve isn’t going to damage your disks unless theres dust and crap in there, though I’m sceptical of some of the “gauze” backed folder sleeves. I suppose they are probably better in the case that the sleeve does get a bit polluted.
In a binder full of disks and zipped up, there tends to be some amount of pressure exerted pushing the disks together. When you open certain folder cases it’s even more pronounced towards the spine of the case, and stresses the disks so you have to slightly close the case to remove them comfortably. This is mainly refering to the larger four disk per page folders, and some are better than others for sure. Another problem with them is when they are being filled over time, the disks get a lot of scope for movement if you are using the case a lot.
The DJ case suspends the disks in a file cabinet style, so if kept flat the disks will not be compacted against one another. Theres no flipping through pages. They also look cool as hell, well, I think so.
Actual dvd cases are probably the best storage format, but again there is the problem of the disk flexing as it is removed from the centre holder in the case.