I can't really comment on Cordoba, since we just passed through on our way to Sevilla. That being said, if you have to choose between Granada and Sevilla, I would choose Sevilla without even thinking twice, especially if you are staying in the old Jewish Quarter (Santa Cruz).

I found Granada to be extremely overrated, but then again, that is just my opinion. The Alhambra was pretty cool to see, but I didn't think it was worth making the trip, which was a little out of the way on our itinerary (Madrid-Toledo-Sevilla-Arcos-Ronda-Granada-Madrid). I would have rather substituted Cordoba for Granada, but the Alhambra was up there on my girlfriend's list of things to see, so I had to grin and bear it. All in all, I found the city, sights, and even people to be the low point of my trip. Then again, my girlfriend disagrees with me completely on this so you'll have to take my opinion with a grain of salt.

As for Sevilla, we stayed in barrio Santa Cruz at a quaint little hotel during Semana Santa, and had an absolute blast. It is nice and quaint, and perfect for strolling around and getting lost in the tiny kissing lanes. There are plenty of good tapas bars to choose from, plenty of flamenco show options, and the cathedral is absolutely stunning, especially at night. The Alcazar was closed for the holiday processions while we were there, but it looked nice from the outside.

Well, that's my 2 cents. Hope it helps.