Given that the button now has Touch ID, and all the components within, the physical components of the button (behind the glass) are now
stainless steel. Whereas on the iPhone 5, 4S, 4, etc they were all
plastic. After the user presses the iPhone 5S home button down, and the home button returns home, the
metal components come in contact with the glass. This results in a more audible "sticky" tone. It could have been resolved with some sort of plastic coating atop the stainless steel areas you see around the home button ring.
Comparison of the two buttons.
This is an image of the iPhone 5 button. It's all one molded piece of
plastic.
and the new button of the 5S has a stainless steel "bowl" with a sapphire crystal piece inlayed in the center. The white sapphire crystal covers the sensors beneath it which are housed within the stainless steel "bowl."
Take a plastic fork and tap it on a glass coffee table. Now take a metal fork and tap it on the same table and listen to the difference. That is whats going on with your new iPhone 5S.
This is not a "feature" of Touch ID, but an oversight by Apple.
As for the tactile "feel" of the button itself, Apple may be using switches from different suppliers, or a wider variety of suppliers. Different suppliers equates to slight variances of the "same" part. The home button on my first iPhone 5S felt like crap, this was in addition to the metal "sticky" sound. I was able to get it replaced and now the tactile feel is far superior, but the metal "sticky" sound is still there.