I had 3/16" rock rails (jcroffroad.com) and they stood up to repeated abuse of having the full weight of the vehicle (on the related side) crash down on rocks. The result? Paint damage to the rockers and *zero* deflection of the rail at the impact area.
IMHO, 0.120 wall sounds fine for what you want to do. Think if it this way - if you ever find you need more beef down the road, you can plate the exterior of your rails with 1/4" stock that is easily available in 2" and 6" widths.