Sorry, when I say "version of CUDA" I meant "whatever the hell they have on AMD" :)
Last I heard CUDA will outperform OpenCL on nVidia vs AMD at the same price point generally as a result of CUDA being in house and closer to hardware. As a result if you just care about compute performance you would go nVidia. If AMD offered their own Mantle based compute offering it would probably shift the other way.
The computing model, no, not really anything fundamentally different. It comes to tooling and profiling under Linux. Also, NVidia has slightly beefer cores and fewer ones, where as AMD has more cores (as I heard). Thus, for me, CUDA is a more complete tool-chain with proper compiler (nvcc), profiler (nvprof, nvvp) and libraries (cublas, cudnn, cufft).
Last I heard CUDA will outperform OpenCL on nVidia vs AMD at the same price point generally as a result of CUDA being in house and closer to hardware. As a result if you just care about compute performance you would go nVidia. If AMD offered their own Mantle based compute offering it would probably shift the other way.