Thanks all for your help folks! After reading this and getting some advice from friends who have been to Barcelona recently, we decided to stay in El Born. The Princesa 8 apartment worried me a bit because of the limited natural light and the glass block wall to the corridor. We decided to splurge a bit more than expected and go with Habitat's Born apartment. That also leaves us some flexibility to try to convince a couple of friends to join us for part of our trip.

I will post a full apartment review when we return, in several months. Thanks again!