Ha-Ha, it is so amusing to see people trying to justify one Spanish city over the other. The thing about Spain is that its rich diversity is one of its mighty strengths--one can always find something interesting to discover.
And I, as a person who loves big cities, would head to neither--instead I would be in Madrid for the four or five days, perhaps doing a day trip to one of the nearby historic medieval towns.
By the way, I think Valencia is very pretty, but a bit sedate, and I think Barcelona has a lot of great sights to see, but too many tourists; however, I would go and visit either city (again) if they were on my itinerary. But, I always make time for capital cities!
¡Buen viaje!