Is Damascus steel stronger than normal (carbon/stainless) steel?

No. For a couple of reasons.

Forging a true Damascus blade is a lost art; we just don’t have the knowledge anymore. The way it’s produced today is meant to simply mimic the look of the pattern welded steel. Secondly, the impetus behind the Damascus blades was to make a better blade by folding two or more metals over itself many times to dissipate the metal’s impurities across the whole of the blade, thus reducing weak spots. Then, the blade is acid etched to reveal a beautiful pattern of waving metals. However, today’s basic tool steel is much more pure than anything they were working with centuries ago.