Simultaneously see Eevee and Cycles renderings Since the light rendering is not the same depending on whether we use Cycles or Eevee, I would like to easily compare this difference on a small scene. 

Is it possible to display simultaneously Eevee and Cycles rendering in two different windows instead of having to constantly switch the render engine?
Maybe an old question but worth mentioning that YES, it is indeed possible. Though may be seen as a workaround:
First place all your settings as you'd like them with Eevee set as your renderer. This includes activating AO, screenspace reflections, irradiance/reflection objects etc. Any setting that is relevant to Eevee basically. This doesn't include lights.
NOTE: HDRI will be independant from Cycles world settings if you're using an irradiance object to bake the lighting.
When you have it all set, split the window to have a second 3D view, then switch to Cycles as your renderer. In the one view set the shading mode to rendered (shortcut: Z) which will be Cycles, and set the other shading mode to material preview for Eevee.
In the material preview window, make sure that the extra options &quot;Scene lights&quot; and &quot;Scene world&quot; are checked.