Something inside your analysis is incorrect. If you do not change the loading (simple gravity) of the analysis then the stress should not change. What should change is how far the model deflects though. So, for your two analysis the cantilever beam is correct; applying the same load (assuming the same material density is used for each analysis) should give the same stress and different deflections.
Now, you would have to go back to your simply supported beam setup and understand why the stress changes when you change Elastic Modulus.