The main difference is that a ventilated facade has an air gap between the insulation and the external finish, whereas traditional insulation simply adheres directly to the wall. That air gap is what makes all the difference: it allows humidity to circulate and evaporate, preventing it from accumulating behind the cladding. In Madrid, with the temperature and humidity changes we get, this is pretty relevant for avoiding condensation and mold problems down the line.
Traditional insulation is cheaper upfront, but it tends to trap moisture. With a ventilated facade you also gain in actual thermal efficiency (that air gap acts as a buffer), the facade stays drier and lasts longer without deteriorating, and the finish has less risk of peeling. It's not just about aesthetics, though of course you can choose nice materials too. The investment is higher, but if your house is old and has moisture problems or you want the renovation to last decades without surprises, it's well worth it.
What I'd recommend is that your architect specifies the system they're proposing clearly: not all ventilated facades are the same, and depending on how your house currently is (thick masonry walls, painted facade, etc.) it might make more or less sense to make that investment.