A fuller history: They were approved for a few years (2004-2007) for use in Yosemite, which is a proving ground for bear-resistant containers. In 2007 I believe there were a couple incidents where bears were able to puncture an Ursack and "suck" food out of it. This led Yosemite to ban them from the park (and ultimately some other national parks followed suit). Since then, Ursack has released new versions it claims work better, along with an aluminum liner (that basically turns it into a more traditional container).
In my personal experience, I have used an Ursack with an odor-proof liner (Ursack sells these as well) on the PCT, CDT, and many other trails in black bear and grizzly country. I'm not sure how well the Ursack itself would hold up to a sustained attack by a determined bear. My experience suggests that the odor-proof liner does it's job well enough though - I've had bears and other pests (rats, mice, etc) in my camp and they never seem to figure out where the food is, even if I've left it right by my tent. The worst I've had is mice a couple times nibbling at the seams of the bag (no damage done).
From what I've heard from other hikers, you almost have to "defend" your Ursack from bears. You tie your Ursack to a tree nearer to your camp than you normally would do a hang. If you hear a bear going after it, you're going to have to actually do something - make noise, throw rocks, whatever, to get it to go away. Because the Ursack is a soft container, even if a bear doesn't get in, it's going to slobber all over everything, crush all your food into mushy bits, and generally make a mess.
All that being said, it has one obvious, major advantage over traditional containers - weight :) 7oz vs 2 lbs 9oz for a comparably sized container!