I’d say it’s a couple things:
1. you may need to adjust your objects’ phong tags, or delete them altogether as the objects have all-sharp edges. Could be blurring out some of the detail;
2. in terms of lighting, there are several things you could do to improve it. The quickest thing you could do for a more realistic look would be to use area shadows instead of soft shadows.
I would also activate the Ambient Occlusion (AO) post effect, or put AO in your floor material’s diffuse channel. That provides a GI-like shadow beneath your objects.
Of course you could also use global illumination for the lighting, with an HDRI mapped to a sky object. Results would depend a lot on the HDRI images at your disposal.
3. With respect to the material, you might want to use reflection in place of, or in addition to, specular highlights. If so I’d put a Fresnel shader in the reflection channel. Inside the Fresnel shader check the “physical” box and choose one of the gem types from the drop-down menu.