I've done some shooting with Damascus guns that appear to be in sound condition, but not enough to make any blanket statements of safety or soundness. Every gun, fluid or Damascus is an entity unto itself and two guns by the same maker and only one serial number apart could have barrels from different sources or batches of steel of different quality or metallurgy. We've seen doubles pictured here that have two different makes of tubes on the same gun. I can state that in a couple decades of looking at every double barrel set at every shop or gun show I've attended, I have yet to see a blown Damascus barrel. On the other hand, I have seen quite a few blown tubes of fluid steel and own several myself.
I have three sets of Ithaca Flues barrels, two 20's and a 16 ga. that have one ruptured tube. Two of these were in the vicinity of the forearm and I wonder if the shooter was injured. I keep meaning to "mike" the wall thickness around these ruptures, but I will say that visually, they don't inspire confidence. Still, thousands of these guns have been shot with high pressure factory loads and a friends' brother used to routinely shoot his Dads' 20 ga. Flues with 3" magnum loads. Don't try this at home kids.
Of course, this could simply mean that most blown Damascus barrels get scrapped rather than taken to guns shows to be sold for parts. I would say far more barrels fail catastophically due to obstructions in the bores than from type of construction or presence of pits or pinholes. But all of this is just my opinion based upon my limited observations. As a legal disclaimer I would advise anyone concerned about safety to never shoot their guns: instead they should give their guns to me and then they can't hurt anyone. I'd be interested to hear more anecdotal evidence of what others here have seen regarding barrel failures of different types. All I know is that I was brought up to believe "Damascus bad-- Fluid good", and as a result I passed on buying some guns dirt cheap that would now be worth thousands.
I have read that when Damascus does fail, it tends to "unwind" along the path of the layers and welds and is more likely to open and vent rather than split and fragment. Even so, escaping powder gasses at several thousand psi levels can certainly do harm to eyes and skin. So shooting glasses and a leather shooting glove on the fore-hand probably aren't a bad idea with any gun.
