Eevee render doesn't look like render preview So when I render the model with EEVEE the render output is different from the render preview in viewport. 

Eevee render viewport screenshot:


Eevee render output:


Why are they different?

This last is the output from cycles.

Cycles render:


How do I achieve something like in the first image with EEVEE and Cycles?!?
Check if Ambient Occlusion is on in the Render panel. That might make the object shadows disappear if it's off.