The only advantage is cost, they both do the job. I'm in the KL/Beads are pretty much the same camp. KL has a set point of 67-68% beads can be bought at 60,65 and 70%. For removing excess humidity KL is 10x more effective and to me this is the deciding factor. Ih the Missouri Spring/Summer months I need to remove humidity and KL is the only thing I've found that can handle the job.
Once a month or more you have someone post a "my beads are not working" thread, I have yet to see a KL is not working thread (I bet we'll see one soon though). Of those who dis the KL I'd bet 99% have not tried it. 100% silica is, well, 100% silica whether you call it kitty litter or beads. A rose by any other name is still a rose.
Foam, beads, KL, a sponge, paper towel or an active system (Oasis, Set n Forget) all will keep your stogies at the right humidity with a little effort. Use what works for you and what you feel comfortable using.