I don't see what they can gain from storing masses of old chats and then not allowing users to download them onto new devices. If they kept chats to do analytics on, there's no reason that they wouldn't expose it to users too.
(This may also explain how they survived as a company for so long with so many users and so little revenue. All they're doing is running a few fast servers to shuttle messages back and forth, no storage requirements at all).
On the other hand Telegram does seem to store conversations - if you log in using a desktop app, it will pull down your recent chats.