I would expect the multi-threading synchronization primitives to be quite faster as they can use shared memory area easily. But I suppose you will have to perform speed test to be sure of it. Also, you might have side-effects that are quite unwanted (and unspecified in the doc).
For example, a process-wise lock could very well block all threads of the process. And if it doesn't, releasing a lock might not wake up the threads of the process.
In short, if you want your code to work for sure, you should use the thread-synchronization primitives if you are using threads and the process-synchronization primitives if you are using processes. Otherwise, it might work on your platform only, or even just with your specific version of Python.