Apple's iCloud Keychain can sync passwords between Safari on different platforms... but only iOS and OS X, not Windows.
Also, IIRC, the Windows version of Safari is not very good and is no longer updated.
You could - as you already mention - use Chrome on all devices, and so use Chrome Sync to transfer passwords and bookmarks from Chrome for Windows to Chrome for iOS.
But not Safari...
One way to transfer passwords (not bookmarks) would be
1Password.
It's an excellent programme for password management, and is available for OS X, iOS, Windows, and Android. I have been using it for years.
Like LastPass, it can sync using "the cloud".
But, unlike LastPass (AFAIK), it can also perform a local sync over your own WiFi network, ensuring that your password vault never touches the Internet.
While both services/apps encrypt your data, I'd still rather not have mine go anywhere outside of my control - especially given that LastPass has been breached
before. Same reason I don't use 1Password's iCloud or DropBox sync options.