When we ran sway bars front & rear on our oval track car we used a stiffer bar in the front than the rear, this idea was based off a ch***is design book from the mid 70's.
Elastic roll moment distribution, strictly speaking. Roll couple is the inertial force effectively acting at the centre of m*** together with the opposite reaction forces acting at the tyre contact patch. Take the ground plane as a datum and we've got a roll moment comprising the magnitude of the inertial force and the height of the centre of m*** as moment arm. Hence we are talking about a torque. Take the centre of m*** as the datum and the roll moment can be seen as distributed a**** the tyre contact patches. The distribution is determined by a number of things, and these are what ch***is tuning is all about. Unsprung roll moment distribution depends on the amount of unsprung m***, front and rear, together with the heights of the front and rear unsprung m***es' respective centres of m***. Geometric roll moment distribution depends on the height of the sprung m***'s centre of m*** above the respective front and rear roll centres. Elastic roll moment distribution depends on the amount of roll stiffness available front and rear. Add all three together for front and rear respectively and we get total roll moment distribution. Note that the less any two are, the more precisely we can determine the total distribution by changes to the third. The conventional wisdom is to get rid of as much unsprung m*** as possible and to get the roll centres as close to the road as possible, so that any changes to roll stiffness can be as effective as possible. There are exceptions, like NASCAR where it is normal to derive most front weight transfer from the front elastic moment but most of the rear weight transfer from the rear geometric moment.
Most front suspensions have lower roll centers than the rear, so to get similar roll stiffness you need more anti-roll/sway bar. With a solid rear axle and parallel leaf springs the roll center is where a straight line from spring eye to spring eye crosses the axle (with lowering blocks that changes). To make it a little easier to understand, the roll center is an imaginary point that when sideways or lateral force is applied the body doesn't roll. The center of gravity is where the lateral force actually works, so the difference in heights is the "leverage" that makes a car roll. If the center of gravity was at 27 inches and the roll center was at 15 a 500 pond lateral force would apply 500 foot pounds of torque to roll the ch***is. On a transverse leaf the roll center is about 6 inches higher so the same force would only apply 250 ft pounds of torque to roll the ch***is. Adding a sway bar increases roll stiffness, and is an easy way to tune this. A panhard bar also allows you to raise or lower the roll center and fine tune roll stiffness without changing springs. That's what the NASCAR boys are doing, raising the rear panhard bar loosens the car by increasing the rear weight split and decreasing the front allowing the fronts to grip better. Lowering it does the opposite. So when we went to the parallel springs we lowered the roll center, softening the roll rate. The leaves probably compensate for this somewhat as they add a little roll stiffness, depending on how close to the tires and how stiff they are. Depending on hat's been done with the front the car could become unbalanced. There are so many variables in a street rod you would need to measure everything on the car to predict what you would need. Once you have the car ***embled if the car has excessive (in your opinion) body roll you will want to add roll stiffness. If the car has a tendency to plow the front end you will need to add more rear roll stiffness. If the rear wants to come around you need more front roll stiffness. If the car feels great, leave it alone. Raising the roll center with location, linkage etc, or a rear sway bar can make your car handle better, only if that's what it "wants". That's a very simple way of explaining a pretty complex issue. Hope it helps.