What kind of "stuff" are we talking about here? Pictures, I'd use Google Drive or Photos. App data really depends on the app, though I hear Helium is a nice backup tool. If you have Marshmallow on both, some apps can back up their data to your Google account for easy restoration of settings and saved data but the developer needs to have enabled that capability.
Otherwise, your data from Google apps (mail, contacts, Keep, calendar, Drive) will all sync once signed in to your account.