Definition of 'Price of anarchy'
As hinted in a comment, the problem with using the difference instead of the ratio, is that the difference is not free of the units of measurement while the ratio is. And in general we want to not depend on units of measurement (whatever it is that we measure).  

Although I am not familiar with the literature, I understand that here utility is a fully quantitative, "cardinal" concept. Moreover, there exists the network $G$ whose characteristics generate utility, and then there are the "idiosyncratic" losses, which is the component we want to get out of our sight.  Then why not define a $\text {PoA}$ net of idiosyncratic losses, especially since they appear not to depend on the decision making framework, and so they are the same both in the decentralized set up and in the centralized one?
I mean,

$$\text {nPoA} \equiv \frac {\sum_iU_i -\sum_i\log(l_i) }{U_s - \sum_i\log(l_i)}=\frac {\sum_if_i(G)}{f_s(G)}$$

This seems to me as a meaningful concept to reflect the network contribution to utility and how it changes under the two decision-making cases.