Sorry, wrote that one too fast. I meant that thicker is better in the general sense (not that 3/16ths wasn't thick enough).
I have the Archer ones on the street car and they work fine though I haven't been towed out of any kitty litter or out of a ditch, thankfully.
The ones on the racecar are 1/4 thick and when I'm lazy and only going a mile or two, I use the front one as the tie-down in the trailer. I don't think the front Archer one would handle the downward bending very well.
You'll be fine with 3/16ths but if you have the option to go thicker, go for it.