Luther,
The quad and 4bag systems, by design, have a solid mounting plate between the bags. The nature of this setup allows both bags to be inflated equally to...say... 110psi. When under hard braking, while the single bag systems may unload the rear tire (sometimes called "pole vaulting") leading to that tire loosing traction (skidding), the quad/4bag systems have a single bag for each arm and keep a full 110PSI of down force on both bogie arms, with no pole vaulting effect and little or no transfer of weight to the front arm, thus significantly reducing rear wheel loss of traction. This becomes significant when going to the heavy duty disc systems that can be installed on the front axle (of the rear).
It could be said that the solid plate between the two bags does not allow for a smooth ride over bumps like speed bumps. I have noticed no difference in coach handling between the original or Sully systems as compared to the 4bag over speed bumps. Felt the same to me, and I've tested this on speed bumps at speeds exceeding 30mph. A smooth ride back there.
So, yes, a 4bag/Quad system keeps all wheels on the ground, improving traction/friction for sudden braking.