I assemble a system for GPU password recovery. What video card is better - AMD or NVIDIA?

Generally, NVIDIA is behind AMD as it concerns performance for GPU 
password recovery tasks.

Study the performance table containing data on different video cards:  http://golubev.com/gpuest.htm

You can see in the table that cheaper video cards AMD are better in terms of performance than more expensive NVIDIA video cards. Sometimes they are substantially better.