Difference between .dds and .png as hair texture

Whichever image type you import, the image you see in the game is a .dds based image. If you import a .png into Studio, Studio will make it into a .dds. If you import a .dds image, it will stay a .dds. This is because the game requires .dds. A .dds is a compressed image and a .png is not. The process of compressing the image when saving it as a .dds results in some loss of data. This is why .dds is called "lossy" and it is why .dds isn't the best image format to save with if you're planning on copying that image, making changes to it, and saving it again.

The differences you see in the game between an image you imported as a .png vs. an image you imported as a .dds reflect the difference in Studio's .dds compression and the .dds compression of your 2D editor. In some cases, Studio's compression will be superior and in others, your 2D editor's compression will be superior. Usually, you won't see much (if any) difference at all. However, there will be cases where there is a difference. That is why Studio will accept either .dds or .png. The creator can then choose which compression method gives them the best result.

Based on orangemitten's explanation and my own experience, it is like this:

for hair texture, saving as dds is superior
for makeup and clothing, saving as png is superior

the downside of dds is that you will lose image quality every time you edit and resave it and saving takes a lot more time than for png. Keep a psd file of your texture (or whatever project format your software uses) to prevent this from happening.