Damasteel is made using powder metallurgy and is a combination of RWL34, which is like CPM154, and 12C27, which is similar to AEB-L. Nichols uses AEB-L, 440C, nickel, and 304 for their stainless damascus and manufactures it by forging.
Pattern-welded steel typically performs like its component steels. I would expect 'better' performance from Damasteel, because both of its component steels are suitable for cutlery, while nickel and 304 are not hardenable by heat treat; but you truthfully may not notice.
Personally if I am buying stainless damascus, performance is a secondary concern. People don't buy damascus for performance, they buy it because it's pretty and for the pattern. But if you want performance, Damasteel is probably the best... and you'll pay for the best, for sure; it is substantially more expensive to get than Nichols or Vegas Forge stainless damascus.
Now, that isn't saying anything against Nichols or Vegas Forge. Both put out top quality steel, and a well-made knife out of either will be a well-made and serviceable knife. I own several knives in Nichols stainless.
I also want to caveat this by saying that Nichols also makes some harder-to-get damascus that is actually san mai with stainless damascus cladding over a cutting edge of high-alloy PM steels like Elmax or MagnaCut. Those will, assuming they are treated to optimize performance of the edge steel, probably perform 'better' given the same knife in different materials than Damasteel. But then you're right back in the argument of exactly how much difference you notice between the different high-end PM stainless steels used for cutlery.