We analyze the optical, chemical, and electrical properties of chemical vapor deposition (CVD) grown hexagonal boron nitride (h-BN) using the precursor ammonia-borane ($H_3N-BH_3$) as a function of $Ar/H_2$ background pressure ($P_{TOT}$). Films grown at $P_{TOT}$ less than 2.0 Torr are uniform in thickness, highly crystalline, and consist solely of h-BN. At larger $P_{TOT}$, with constant precursor flow, the growth rate increases, but the resulting h-BN is more amorphous, disordered, and $sp^3$ bonded. We attribute these changes in h-BN grown at high pressure to incomplete thermolysis of the $H_3N-BH_3$ precursor from a passivated Cu catalyst. A similar increase in h-BN growth rate and amorphization is observed even at low $P_{TOT}$ if the $H_3N-BH_3$ partial pressure is initially greater than the background pressure $P_{TOT}$ at the beginning of growth. h-BN growth using the $H_3N-BH_3$ precursor reproducibly can give large-area, crystalline h-BN thin films, provided that the total pressure is under 2.0 Torr and the precursor flux is well-controlled.