With coarse structures (something that spans at least several pixels), the file from the E model would show sharper edges (more edge contrast). With some capture sharpening, the file from the non-E should provide the same result. Both will capture the same detail (as these are coarse structures).
Once you get to very fine structures, something just one or two pixels across (fine grain of sand, tiny spectral highlight etc), then the E model may capture more detail, but at the expense of accuracy. In other words, some of that detail may be faux (not real), and some may show up with a different color than the real subject. In most cases, such artifacts are not visible as such and may actually give the impression of a sharper and more detailed image (looking "nice"). The most egregious and example of faux detail is moire, of course. As it is caused by a repeating pattern of fine detail it is very visible (unlike some "wrong" pixel here and there), but it is also quite rare.