We performed charge-exchange experiments with the electron-beam ion trap and an x-ray calorimeter spectrometer at the Lawrence Livermore National Laboratory. We compare the relative strength of the high-n Lyman series emission for different combinations of ions and neutral gases. Theoretical predictions show good agreement with experimental data on the relative capture cross section as a function of principal quantum number n; however, the few published predictions of the distribution of captures as a function of orbital angular momentum l do not agree with experiments. Our experimental results show that the relative strength of high-n Lyman series emission varies more widely than previous experiments have found and models predict. We find that hardness ratios from charge exchange with helium and molecular hydrogen are more disparate than charge exchange with many-electron neutral species, which is likely due to differences in the relative importance of multielectron capture. We also find that there is no clear scaling of the hardness ratio with the ionization potential of the neutral species, the number of valence electrons in the neutral species, or the atomic number of the ion.