There's a great old post by master restorer Paul Pratt, where he addresses this exact issue. Here's
the link. Scroll down and look for the subhead: "When restoration becomes 'over restored.'"
My preference might be to repaint or powder coat the black side panels, to leave the chrome alone, and to try and clean up the gold trim. If a piece of gold trim is badly corroded (can't see in your pix), I might re-plate or refinish that part, matching it closely. Otherwise I agree with the others, clean and polish. Polishing on a big buffing wheel can also be overdone for a mirror-like shine that wears away the surface. For polishing my emphasis would be on good clean-up while retaining the original texture of the surface.