Both metals look white. Both are traditional bridal choices. They are not the same thing. Here is the comparison you actually need.
Price
Platinum is more expensive per gram because it is a rarer and denser metal. A comparable platinum band typically costs 50–80% more than the same design in 18ct white gold. The density is part of the point — platinum rings feel substantial on the finger.
Colour
Platinum is naturally white. It never needs plating. Over decades it develops a soft matte "patina" that many people prefer to the original bright shine. White gold is naturally a pale grey; it is rhodium-plated to look bright white. The plating wears through in 1–3 years and the ring picks up a creamy tone. Re-plating is cheap (€30–€60 a time) but it is a recurring job.
Durability and wear
Platinum is softer than 18ct gold in absolute terms, but because it is denser it wears more slowly in practice. It also scratches in a way that moves metal around rather than removing it — that is where the patina comes from. White gold is harder and holds a sharp polish longer, but the plating wears off.
Allergies
Platinum is one of the most hypoallergenic metals available. White gold alloys often contain nickel, which is a common contact allergen. If you or your partner have sensitive skin, platinum is the safer default.
Which to choose
Choose platinum if: you want a white metal you never think about, you have sensitive skin, or you want the premium feel. Choose white gold if: you want to save a meaningful amount and you are happy to re-plate every couple of years.