Helium nanodroplets ("HNDs") are widely used for forming tailor-made clusters and molecular complexes in a cold, transparent, and weakly interacting matrix. The characterization of embedded species by mass spectrometry is often complicated by the fragmentation and trapping of ions in the HNDs. Here, we systematically study fragment ion mass spectra of HND-aggregated water and oxygen clusters following their ionization by charge transfer ionization ("CTI") and Penning ionization ("PEI"). While the efficiency of PEI of embedded clusters is lower than for CTI by about factor 10, both the mean sizes of detected water clusters and the relative yields of unprotonated cluster ions are significantly larger, making PEI a "soft ionization" scheme. However, the tendency of ions to remain bound to HNDs leads to a reduced detection efficiency for large HNDs containing >104 helium atoms. These results are instrumental in determining optimal conditions for mass spectrometry and photoionization spectroscopy of molecular complexes and clusters aggregated in HNDs.