Summary: Use VS Code's built-in Setting Sync for most cases. Use Khan's Setting Sync extension if you require multiple profiles (ie multiple settings) or you are running open source version of VS Code (such as VSCodium).
Before the official VS Code's version was released, the most popular way to sync VS Code settings across computers (and across platforms like Windows, Mac and Linux) was possible with Shan Khan's Settings Sync - Visual Studio Marketplace. This extension works really well, but it requires the users to set up their Github as it saves the settings to their private Gist.
VS Code had recently released its own Settings Sync, which unfortunately uses the same name as the extension, causing some confusion amongst the users. The built-in sync requires account in MS or Github. According to the VS Code documentation, it is completely different from Khan's Settings Sync extension. Now that the VS Code has introduced the feature of syncing, the writing might be on the wall for the extension. However, the extension has other features that is not available in the VS Code, so I think it will continue to be used and updated.
Khan's Settings Sync extension might be preferrable over the VS Code's built-in sync for some cases. Khan's Setting Sync can have multiple profile. Also OSS version of VS Code such as VSCodium doesn't include this feature, so the extension might be the only way to have this feature. Also, it is sometimes useful to be able to see different versions of your settings in Github Gist, as it maintains versioning. Finally, Khan's Settings Sync is also available for Azure Data Studio, which is based on VSCode.
