It will use the first compiled version.
There are other nuances in terms of re-execution. For example, depending on the stored procedure, SQL Server might (and hopefully will be able to use) the cached query plan. But if there is dynamic SQL, certain types of logic, or large data changes (among other things), then the DB engine will need to rebuild the query plan.
But stored procedure 'compilation' is done at the time of creation. Unless you specify for it to do otherwise (see here) then it will not recompile.