The nature of the hydrogen sublattice of an HCl-doped ice VI sample after cooling at 1.8 GPa has been a topic of recent interest. The samples are interpreted either as the new H-ordered ice phase ice β-XV with a thermodynamic stability region in the phase diagram [T. M. Gasser et al., Chem. Sci., 2018, 9, 4224], or alternatively as H-disordered, deep glassy ice VI [A. Rosu-Finsen and C. G. Salzmann, Chem. Sci., 2019, 10, 515]. Here we provide a comprehensive Raman spectroscopic study on ice β-XV, ice XV and ice VI, with the following key findings: (i) the Raman spectra of ice β-XV differ fundamentally from those of ice VI and ice XV, where the degree of H-order is even higher than in ice XV. (ii) Upon cooling ice VI there is competition between formation of ice XV and ice β-XV domains, where ice XV forms at 0.0 GPa, but ice β-XV at 1.8 GPa. Domains of ice β-XV are present in literature "ice XV" at 1.0 GPa. This result clarifies the puzzling earlier observation that the degree of H-order in ice XV apparently improves upon heating and recooling at ambient pressure. In reality, this procedure leaves the H-order in ice XV unaffected, but removes ice β-XV domains by transforming them to ice XV. (iii) Upon heating, the samples experience the transition sequence ice β-XV → ice XV → ice VI, i.e., an order-order transition at 103 K followed by an order-disorder transition at 129 K. The former progresses via a disordered transient state. (iv) D2O ice β-XV forms upon cooling DCl-doped D2O-ice VI, albeit at a much lower pace than in the hydrogenated case so that untransformed D2O ice VI domains are present even after slow cooling. The librational band at 380 cm-1 is identified to be the characteristic spectroscopic feature of deuterated ice β-XV. Taken together these findings clarify open questions in previous work on H-ordering in the ice VI lattice, rule out a glassy nature of ice β-XV and pave the way for a future neutron diffraction study to refine the crystal structure of D2O ice β-XV.