Solid bars are stiffer if the diameter is the same. I know the 1-5/16" "thin-wall" Helwig bar is comparable to a 1-1/8" solid... The rate of it would depend on the wall thickness, which of course would depend on the manufacturer.
The big advantage to hollow bars is that they are are much lighter weight, given the same
rate. As the metal gets farther from the centerline, it takes less metal to do the same amount of work. The metal near the center of a solid bar does very little to add rate, but adds just as much weight as if it were placed elsewhere.
A secondary advantage is that they look really big, without actually having so much rate that they take too much compliance out of the suspension. This pleases the "if some is good, more is better" crowd.

I actually prefer a smaller solid bar for this reason... the whole "how the heck is he doing that with a stock sway-bar?" is worth a few pounds to me.
The best thing to do before ordering would be just to ask the manufacturer what rate it compares to in a solid bar, but if you want to play around with the math, rate increases by diameter^4.
Solid 1" bar: 1x1x1x1 = 1
Solid 1.125 bar: 1.125x1.125x1.125x1.125 = 1.60 times stiffer than a 1" bar
Solid 1.25 bar: 1.25x1.25x1.25x1.25 = 2.44 times stiffer than a 1" bar
A 1.25 hollow bar with 0.125" wall thickness would be 1.44 times stiffer than a 1" solid, using only 56% as much material (weight) of what a 1" solid does.
Crap, I think I just convinced myself I need to spend money on a new hollow bar.