Google is an example of something that won out because it was the better application, search wasn't a largely cluttered field though and they were taking a largely new angle on in. If your putting out another social networking app at the moment though it's unlikely to catch on just because it is the better designed app, just look at the troubles something as large and as well backed as friend feed is having.
Also, "good" and "well designed" are totally subjective- everyone thinks their own baby is beautiful and brilliant. The problem may be that your product isn't as amazing as you think it is, not that someone outmarketed you. Good marketing/PR can give you a quick jump out of the gate, but the best product eventually wins the race. (Isn't that the lesson of the "shark fin" alexa graph?)