For a good older multi-coated lens, the difference may be much smaller than many people expect. Multi-coating technology was already well developed decades ago; for example, Pentax’s Super-Multi Coating dates back to the early 1970s and is fundamentally the same kind of anti-reflection approach still used today.

The main purpose of lens coatings is to reduce reflections between glass surfaces, which helps reduce flare and ghosting and improves contrast. There is a very small light-loss tradeoff, but it’s generally considered worthwhile.

Coatings are not a primary factor in bokeh. Bokeh is influenced much more by the optical design and aperture shape. Sharpness is also mainly determined by lens design, alignment, and quality, though reduced flare can make an image appear clearer or higher in contrast.

With filters, the same principle applies: adding more glass can increase reflections, so coatings on the lens and on the filter can matter for flare/ghosting and contrast. In short, coatings mostly affect flare resistance and contrast, not the basic character of bokeh.