Numerous neural network circuits and architectures are presently under active research for application to artificial intelligence and machine learning. Their physical performance metrics (area, time, energy) are estimated. Various types of neural networks (artificial, cellular, spiking, and oscillator) are implemented with multiple CMOS and beyond-CMOS (spintronic, ferroelectric, resistive memory) devices. A consistent and transparent methodology is proposed and used to benchmark this comprehensive set of options across several application cases. Promising architecture/device combinations are identified.