In arteries, the main structural difference is the thickness of the arterial wall, due to an increased amount of smooth muscle, arteries have much thicker walls than both veins and capillaries to ensure they can withstand pressure exerted by the blood and to also maintain this pressure as blood travels around the body.
In veins, the main structural difference is the presence of valves. Valves ensure blood flows in one direction and that backflow does not occur, ensuring deoxygenated blood reaches the heart. Whilst in capillaries, their tiny lumen means red blood cells are forced to travel single file, this means there is more time for diffusion of oxygen into the body's cells.