None of the answers really address the issues that could be tied up in this question.
To keep it simple if we only consider 'Engineering' Stress Strain' Data then:
For the Brittle Elastic Solid you describe the ratio of tensile strength to yield strength will be 1.00.
If the material were, however, Elastic-Ideally Plastic ie non-work hardening the ratio would still be 1.00. (Plasicine would have this behaviour)
Clearly the two materials are very different and if you compare the True Stress vs True Strain Curves the behaviour would be very different but it would be very difficult to produce this data.
Clearly most metals are Elasto-Plastic Work Hardening Solids and there is a huge amount of data needed to fully define and understand their behaviour across a range of engineering applications.
Ductility is sometimes considered a guide to a material's impact strength, sometimes its ability to be used for pressing or other process involving sheet metal deformation and generally requires information with regard to the level of strain that is associated with this deformation. Again bend test data can be used to give some subjective guide to performance.
If you are concerned about Fracture Tougness you will need Charpy Impact Data or better still KIc values. If you are worried about low temperatures the FATT data will be good to have.
If you are concerend about pressings you will need either Forming Limit Data of Work Hardening Exponents etc, etc.
You need to consider the application and seek the relevant data to be confident.
I think that if if you try to define a single non-dimensional parameter you will potentially make disastrous selections.