I enjoy the nice big stable platform pedals on my road bike, but the road shoes and big cleats make my road bike inconvenient for anything but sporty, fast rides on smooth roads because walking is uncomfortable, bordering on dangerous.. And as far as I know, the advantage is all in my head. I doubt if a finely tuned athlete did a 40 Km time trial on a bike with high-performance road shoes and pedals, then with the same bike with MTB pedals and shoes that there would be a measurable difference in performance.'

IF you ever get off your bike to walk more than 'from your car to your bike' then mtb style shoes and small-cleat/spd style* shoes and pedals are the best choice. I suppose the best road style shoes and pedals might be a tiny bit lighter than the mtb style equivalent, but not so that you would ever notice.

Another advantage of road style pedals is usually increased cornering clearance because they have a much lower profile due to not having a mechanism or platform on the back side. This is only an advantage if you are a high-performance rider or are competing in criteriums or races where it is advantageous to pedal deep into corners.

*SPD pedals are by far the most common shoe/pedal interface, but not the only one that uses a walkable shoe and cleat. Crank Bros., Time, Speedplay, Look all make competing designs that have advantages and disadvantages compared to Shimano' SPD.