Convention for logging within nested try catch blocks

I've looked at this question but it doesn't really help solve my dilemma.

System 1 calls system 2 within a try catch, the method in system 2 has it's own try catch, which sadly handles an exception but does not re-throw it. So my question is: Which system should log it? Each system has it's own logging files.

Sample:

Class System1{
Public void DoSomething(){
    Try{
        var sys = new System2();
        sys.ExecuteMethod();
    }
    Catch{Exception e){
        logger.log(e);
    }
}
}
// ------IN A DIFFERENT SYSTEM ON A DIFFERENT MACHINE------
Class System2{
Public void ExecuteMethod(){
    Try{
        throw new Exception("Test Excpetion");
    }
    Catch{Exception e){
        logger.log(e);
    }
}
}
}