The aim of this work is to quantitatively compare two commonly used beam quality indices, IPR(20/10) and %dd(10)x, with respect to their ability to predict stopping power ratios (water to air), s(w,air), for high-energy x-rays. In particular, effects due to a varied amount of filtration of the photon beam will be studied. A new method for characterizing beam quality is also presented, where the information we strive to obtain is the moments of the spectral distribution. We will show how the moments enter into a general description of the transmission curve and that it is possible to correlate the moments to s(w,air) with a unique and simple relationship. Comparisons with TPR(20/10) and %dd(10), show that the moments are well suited for beam quality specification in terms of choosing the correct s(w,air).