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MPI is a message passing paradigm of parallelism. Here, you have a root machine which spawns programs on all the machines in its MPI WORLD. All the threads in the system are independent and hence the only way of communication between them is through messages over network. The network bandwidth and throughput is one of the most crucial factor in MPI implementation's performance. Idea : If there is just one thread per machine and you have many cores on it, you can use OpenMP shared memory paradigm for solving subsets of your problem on one machine.
CUDA is a SMT paradigm of parallelism. It uses state of the art GPU architecture to provide parallelisim. A GPU contains (blocks of ( set of cores)) working on same instruction in a lock-step fashion (This is similar to SIMD model). Hence, if all the threads in your system do a lot of same work, you can use CUDA. But the amount of shared memory and global memory in a GPU are limited and hence you should not use just one GPU for solving a huge problem.
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