This totally depends on what, exactly, we're talking about.
Most "Damascus" knives you see advertised are in fact only clad in layered steel (what they call Damascus steel). Those knives that are clad in Damascus steel are no better or worse performance wise than if the knife was clad in a mono steel. It would just be for pure aesthetics.
A knife that is truly layered steel (Damascus) at the cutting edge will have different performance than a knife made with a single steel. The layered steels are different and this is done so that the pattern can be showed off. Devin Thomas's Damascus is a prime example. The pattern you see in the blade is caused by acid etching the blade/steel. One steel reacts to the etching one way and the other reacts a different way and thus you can see the pattern caused by Devin's work. So the edge is made up of two (or more) steels and each has it's own characteristics. The edge is essentially a combination of the characteristics of both steels. The advantages/disadvantages of a Damascus steel edge could/will be discussed for an eternity.
BTW, there are very few kitchen knives made today that are Damascus at the cutting edge. You'd have to find a custom knife maker most likely. Almost everything Japanese made that you can find advertised as Damascus is Damascus clad with a mono steel core. There are a number of makers in the US making Damascus blades though....Devin, Burke, Ealy, Fowler, Rodrigue...even me....but I have to buy my Damascus from Devin. Stupid power hammer and forge won't fit in my garage.