Scenario: You have a computationally expensive function that should benefit from being pushed out to a plugin rather than being run via script. An example could be A* navmesh searches for a large number of agents.
There are two possibilities for implementing plugins: A CLR-compatible (Mono) library or a native library.
Question: Will the performance difference be the standard CLR versus native performance difference you get in any situation, or are there other performance considerations that need to be taken into account. E.g. Is the CLR plugin treated differently by Unity than the native plugin in a way that impacts performance of the two differently?
CLR plugins are much easier to write, and work as if you were writing scripts straight into Unity - There isn't any difference there, besides consolidating things into a single assembly
Native plugins can be faster, but you have to do a lot more work with marshalling (managing the native/managed interop), as well as being required to use unity pro to develop and compile.
The best bet is to start off with managed/CLR, and move onto native plugins if you really need to
Edit to answer the question in your last paragraph:
There should be no difference in the standard CLR vs native performance difference - CLR is treated as usual in any CLR situation (Identical to including a CLR library into any other .NET project), native uses p/invoke as it usually does