Local storage is more secure, but it also has its downsides. When you sync your passwords locally, your data never actually leaves your device — but this also makes it difficult (or at least inconvenient) to sync your passwords across all of your devices. Top brands like 1Password offer users the option to choose whether to store passwords locally or on their servers.
On the other hand, cloud-based password managers like Dashlane use very secure servers to store encrypted user data (the data is encrypted using military-grade encryption, which has never been breached). And because user data is online, in the cloud, these password managers automatically sync all your passwords, so you can easily and conveniently access your password vault on all your mobile and desktop devices.