Amorphous TiO2 nanotubes were irradiated in-situ in a transmission electron microscope (TEM) with Kr+ ions at energies of 46 keV, 150 keV, and 1 MeV and with 46 keV Xe+ ions, to investigate the structural and morphological evolution of the nanotubes under irradiation. At all irradiation conditions, amorphous TiO2 nanotubes exhibited significant morphological instability, and tended to undergo volumetric swelling with increasing ion counts, often until collapse of the original nanotube structure. Molecular dynamics (MD) simulations confirmed that irradiation-induced defects can explain the observed swelling. Structurally, nanotubes remain amorphous following all Kr+ irradiation conditions, but irradiation with 46 keV Xe+ leads to the formation of anatase nanocrystallites. Importantly, through systematically varying ion energy and ion species, we try to elucidate the influence of nuclear and electronic stopping power on ion irradiation induced changes. By contextualizing these results within the existing literature, we propose that the observed changes in TiO2 nanotube morphology and structure could be due to a competition between two mechanisms: (1) disorder-induced swelling and (2) irradiation-induced amorphous-to-crystalline transformation.