We have used Raman spectroscopy to study the behavior of multi-walled boron nitride nanotubes and hexagonal boron nitride crystals under high pressure. While boron nitride nanotubes show an irreversible transformation at about 12 GPa, hexagonal boron nitride exhibits a reversible phase transition at 13 GPa. We also present molecular dynamics simulations which suggest that the irreversibility of the pressure-induced transformation in boron nitride nanotubes is due to the polar nature of the bonds between boron and nitrogen.