Depends on your tastes and preferences. Do you want to be right in the center of everything, at the touristic "ground zero" of all the action? Being there comes with some noise (I have indelible memories of trying - and failing - to sleep in my charming B&B in the center of the Gothic Quarter...there was the normal street noise that only abated slightly for a few hours overnight, but the drunk who kept screaming all night long never quit...).
Personally, I like being close to the attractions and all the action, but not necessarily completely surrounded by it all, and I value quiet during quiet hours. You can find some of that in either of the two neighborhoods you mention, but you will want to investigate exactly how far from all the action your window would be (probably easier to find more quiet corners in Eixample).