Platinum is naturally white and does not tarnish.

Platinum is rare, heavier,  durable, more dense, and more expensive.

Platinum can be dented.
Platinum is hypoallergenic because of its purity.

White gold wears off and fade to a yellowish tint, re-plating will make a white gold jewelry looks new.

White gold is naturally yellow.

White gold is composed of gold, alloy, and is rhodium plated to achieve the white color.
Gold can be scratched.

18karat white gold is softer and can easily fade because of its 75% gold content. This has a higher value than 14k.
14karat gold is harder and cheaper because of its 58.5% gold content.