Put another way, I think I am aware of things even if not attending to them, however by attending to a thing I am definitely more aware of it. But in this sense, am I aware of a thing because I attend to it, or am I attending a thing because I am aware of it? The latter seems more reasonable. Therefore I think Graziano's idea is more consistent because in such an interpretation the process of attention leads to both background and foreground awareness as consciously discerned, whereas Prinz's idea suggests only foreground awareness can be conscious. Marrying the two ideas as I suggest above seems to resolve that.
Naively, there could be both. A sudden loud sound in the coffee shop will draw your attention to it even though you haven't been paying attention. On the other hand, there are sounds all around you which you don't notice until you pay attention to them. You can search for "bottom-up" and "top-down" attention. It's also an issue in machine vision.