What do you mean by "element-to-node-ratio"? The number of nodes per element? That surely has an influence because it determines whether your displacement function on the element is linear or quadratic. In elastic problems, quadratic is usually better; linear may be problematic especially in bending ("shear locking" or "hourglassing" may occur, depending on the integration scheme).
The quality of the FE solution is dependent not only on the mesh but also on the exact stress field. If your problem only involves a constant stress field then a single element (linear or quadratic) will capture the exact result. If the solution is more complicated, which is generally the case, then you will need to look at convergence studies. There is no way, a priori, to judge the quality of a mesh. This may only be done after the solution has been obtained.
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