Well, obviously the aircraft with mode C only will get no warning of the other traffic.
The aircraft equipped with mode S will receive
- traffic advisory (TA) for targets equipped with mode A upwards,
- resolution advisorys for targets equipped with mode C upwards
- coordinated RAs for targets with mode S (coupled with a functional TCAS that is).
To get back to your original question there would be no benefit to neither aircraft if one was equipped with mode S but no TCAS rather than mode C only, since this would make the coordination function of mode S useless (you won't ever get to know "your" part of the resolution), basically making it a more expensive mode C model.