While the colors of platinum and white gold are certainly very similar, they are not identical, as you can see it yourself when trying them side by side. White gold is slightly more silvery and platinum is more gray. Both accent white diamonds beautifully, but should probably not be mixed in your engagement ring / wedding ring set. Stay consistent with the metal you choose, or they won’t look like they match (especially over time).
White gold is made up of a mix of yellow gold and some other white metal (usually silver, nickel, or palladium. So, there is no such thing as “pure” white gold. Every few years it should be re-dipped in order to retain its white color and shine, otherwise it will start to revert back to the color of the main ingredient: yellow gold. This seems like it can be a hassle, but it’s a fairly simple and inexpensive process.
Platinum has a natural grayish white color. In order for Platinum to be sold as “platinum”, it must have at least 90-95% of platinum. If it’s less, it will be sold as platinum alloy. Over time, platinum’s color will not fade towards a yellowish color like white gold will, but as years go by its shiny finish will start to turn into a dull satin type of look (which actually makes the diamond look even brighter!). If you prefer the shiny look, platinum can be shined by a professional jeweler to bring back the original shine.