The white-metal question is really platinum versus white gold; the color question is white versus yellow versus rose. Here's the honest comparison.
Platinum
Naturally white forever, hypoallergenic, and denser — prongs hold stones more securely for decades. It scratches into a soft patina rather than wearing away, and costs roughly $300–500 more per ring. The heirloom choice.
White, yellow, and rose gold
White gold is rhodium-plated for brightness and wants a $40 re-dip every couple of years. Yellow gold is the classic that hides scratches best and flatters warm skin tones; 14k wears harder, 18k runs richer in color. Rose gold's copper alloy makes it the most durable gold — and the most distinctive.
Practical rule: platinum for the engagement ring's stone security if budget allows; matching gold color to the jewelry she already wears beats every other consideration.