To ensure the dwg eport and the Revit sheets look exactly the same you'll need to use the following export settings.
Revit is WYSIWYG, (What you see is what you get), Once you have set up your views and they look exactly how you want them, follow this process.
From the application menu (The big 'R') select export, then dwg.
From the dialog, select the 3 dots next to the drop down for 'Select Export Setup'
Export Layer Options should be set to 'Export all properties BYLAYER, and create new layers for overrides'. This ensures of any elements have manual overrides, filters or other changes in the view to be exported the changes are retained.
We use AIA layers, but it's not important, just pick one that suits you.
On Line tab, pattern tab, text and fonts, ensure all are set to {Automatically generate ...}
Colors tab needs to be set to Trues colour if you want colours to map the same
Solids Tab, ACIS solids
Units and Coordinates, we use shared basis.
General Tab, we select export rooms option, we hode scope boxes, reference planes and unreferenced tag, but leave 'Preserve coincident lines' unticked to ensure minimise duplicate lines.
Hope this helps