From the point of view of the fish there’s very little difference in terms of shelter potential and for some species that eat live plants but appreciate hiding places they can be a massive help. They also serve to create a lush appearance where conditions may not favour the growth of real plants such as dimly-lit tanks or those with strong water-movement. Artificial plants can also be used alongside real plants to add a bit of variety.
It could be argued that artificial plants provide a surface for filter bacteria and like it or not, serve to trap detritus as well. What they can’t do is function in some of the amazing biological ways that living plants do. Healthy plants absorb pollutants produced by the fish population, such as ammonia, as well as the nitrates and phosphates that result from the functions of filtration and promote the growth of algae. Under sufficient lighting they also produce oxygen and remove carbon dioxide but it should be noted that this process is reversed overnight and oxygen levels can fall to very low levels in densely-planted aquaria with significant fish populations and low circulation.
Plants also have requirements and they need feeding to ensure they have all they need to function. Elements such as Iron are vital and a good aquarium plant fertiliser makes a huge difference to the growth of aquatic plants. CO2 supplementation can also help guarantee a healthy underwater garden.