Just to put the thicknesses into a more american-friendly form for those of us that are not very good at trying to envision anything in the metric system 4mm = ~ 1/6 inch and 6mm = ~ 1/4 inch (a little less).
When you order your sandals from invisible shoe, they come in a kit, so you have to decide where you want to put the hole between your toes which allows you to make it custom to your feet. You may need to trim some of the rubber from the sides if you have more narrow feet, I didn't, because my feet are boats. Next, follow the instructions found on the site to tie them up to your feet, or you can just make up your own ways to tie them, it really doesn't matter as long as they are comfortable. Take your time to make sure that they fit the way you want them to and are comfortable, it is worth it when you are out on the trail.
Anyway, after taking some time to try out the 4mm Connects, I have a few things to say. Since the sole is significantly thinner than the 6mm huaraches, it is more floppy. I find that it slaps around on the ground a lot more as I am running, this may be due to it being a little too loose on my foot which I am going to try and change this week and give you guys an update. It is harder to keep it from folding under and staying close to your foot. I really love the 6mm Contacts because of the way that they form to your foot and stay there. When running in them, I almost feel like I am running completely barefoot because they stay put so well on my feet that I hardly notice them, where the 4mm's were more floppy and harder to manage. As far as the 6mm being more "padded" or offering more protection against the ground than the 4mm's, I really didn't notice a difference. I think that both are thin enough that they truly don't offer any cushion (which is good), and are very comparable in the amount of protection that they offer. I HIGHLY recommend the 6mm Contacts for any barefoot runner looking for a little protection on those gravely, glassy or hot roads. I really love mine and wear them often. As I have said before, I love to take them on a barefoot run with me in my hands and when I encounter areas that are tough on the feet, I throw them on so I don't tear my feet up. I mostly do this because of a couple bad experiences with glass/slivers/tiny sharp objects while running on the side of a busy road or an old wooden bridge.
Now it's time to go order some of your own! You won't regret it!