AMD cards offer comparable compute performance and are sometimes even better. What AMD lacks, though, are ready-to-use software packages like CUDA, cuDNN, cuBLAS, and the like.
NVIDIA basically bought their way into the research community and solidified their strong foothold by keeping CUDA proprietary.
It's fascinating how other companies (Microsoft) get bashed on a regular basis for using the exact same tactics (see Direct3D vs OpenGL on Windows), while people are perfectly fine with NVIDIA doing it...