I am fortunate enough to have a garage - so my Vespa is spoiled. I would always favor a breathable cover if the scoot must be left out in the elements.
On extended rides, I don't travel with a cover - I simply wipe the dew off with a clean rag. Interestingly, I find that many of the hotels we have stayed at actually have clean old towels in the entry way for bikers to wipe off their two wheelers. Smart hotel managers, by doing this they slow down hand towels being stolen from their rooms.
Fledermaus may have called it right. Constant Sun Exposure may cause more problems. While living in Europe, I actually kept my Ducati in my apartment to avoid exposure to the elements and to prevent rampant theft in Southern Italy.
Bob Copeland