Rubicon has the red shocks.
Heavy-Duty is just marketing hype. I believe the Rubi's "Sport Suspension" has slightly stiffer springs/shocks.
The real difference is in the transfer case. The Rubi has a 4:1 TC ratio, the Sahara has a 2.72:1 TC ratio. This means that when you have it in 4LO, the Rubi can crawl over terrain at a much slower / controlled rate. This is great for rock crawling.
The Rubi also has the electronic sway-bar disconnect feature. With a push of a button, it will let the front suspension droop about 20% more for better off-road suspension articulation, allowing you to maintain the tires on the ground for better traction.