The german style is a bit different. Try them both maybe. I've tried wearing footwraps, but it doesn't fit my feet and boots. This style of footwraps makes for a lot of extra bulge under the vamp; I have a high bridge and my boots are narrow in that area.
The proper material would be some kind of linen/wool blend which is not easy to find. You can try linen or cotton blends though.
The main advantage of footwraps is for long term living in the field; they dry quicker, are easier to wash, last longer than socks (pure wool socks as they had at the time anyway). They're harder to put on, and if you fuck it up you will get sore spots. Since the material absorbs a lot of moisture, yet dries quickly again, you have more options for keeping your feet dry... but on a short hike or with enough time, you can do the same by switching socks.