Well, there's no comparing Barcelona and Girona -it's a bit like comparing pears and apples as they're both of very different size hence the availability of things to do/see greatly varies. Having said that, Girona, as I mentioned in the other post, it's considered the second capital of Catalonia after Barcelona, not for its size (merely under 100.000), but for its historical and economical importance. It's a "fully functional" city... she has a bit of everything and the central district, the Old Town, is a gem of the medieval. And you'd have also plenty of other places to visit in nearby excursions, like Besalú, Cadaqués, Empuries, Roses, Calella de Palafrugell, etc. after all, 5/6 days is not "that" long if you think about it. Have a look in the website of Costa Brava, the name of the region where Girona is located: http://en.costabrava.org/
So, there's really no answer for you, the two destinations are worth spending days in. To me it'd be like choosing to spend a week in NY or a week in say Seattle (to name two different 'ambiances')... there's no possible comparison, it all depends on what you want to see.