We report a comparative study of the crystal structure and magnetic properties between (001) oriented epitaxial BiFeO$_3$ films grown on NdGaO$_3$ and SrTiO$_3$ substrates without any magnetic parasitic phase. The 15 nm BiFeO$_3$ film deposited on a NdGaO$_3$ substrate shows substantially high magnetization (∼250 emu/cc) as compared to an identically thick BiFeO$_3$ film (∼100 emu/cc) deposited on a SrTiO$_3$ substrate. Detailed structural analysis revealed that the high magnetization is associated with a monoclinic (Cm) like distortion of the BiFeO$_3$ crystal structure. We corroborated our experimental findings with first principles density functional theory calculations which suggested a saturation magnetization (266 emu/cc) close to the experimentally obtained one and a ferromagnetic ground state with the high spin moment in the Cm phase.