Amazon is the only one, yeah. You can sideload books, of course. But that doesn't give you syncing.
In general:
A number of iOS/Android apps can sync/backup their own data, so other instances of said app can be identical.
I believe you can read books uploaded to Google Books on both Android and iOS. but it and Amazon are the only services I know of which do 3rd-party ebooks on both. And only Amazon adds an e-ink ereader to the mix.
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