What version of Blender and Verge3D are you using. Not that it is really that important but it allows those trying to help out to elimiate that as a source of issue if any.
The results you are getting in Cycles, minus the light bounces should be repeatable in Verge3D. Not as perfect but close. Keep in mind that EEVEE is an interoperation of what you will see in Verge3D it is close but not exact.
Things that can impact your EEVEE look. Color management – make sure you are on Standard.
Are you using an Environment map in EEVEE to light the scene? Try turning it down.
Try with and without AO.
Try a different materials for your white objects…try a basic diffuse shader and see if you have a shader issue?
Try changing the angle of the sun light.
Take a screen shot of your blend scene or post a blend file and I am sure someone here can help you out.
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