The computational efficiency and energy-to-solution of several applications using the GAMESS quantum chemistry suite of codes is evaluated for 32-bit and 64-bit ARM-based computers, and compared to an x86 machine. The x86 system completes all benchmark computations more quickly than either ARM system and is the best choice to minimize time to solution. The ARM64 and ARM32 computational performances are similar to each other for Hartree-Fock and density functional theory energy calculations. However, for memory-intensive second-order perturbation theory energy and gradient computations the lower ARM32 read/write memory bandwidth results in computation times as much as 86% longer than on the ARM64 system. The ARM32 system is more energy efficient than the x86 and ARM64 CPUs for all benchmarked methods, while the ARM64 CPU is more energy efficient than the x86 CPU for some core counts and molecular sizes.