I've used OfflineIMAP for many years, and recently (less than a year) moved to mbsync. It's much faster, and the end result is largely the same (I did some sanity tests, downloading both and comparing).
I'm not exactly sure if you can migrate to a new provider by providing the mailbox yourself, but you can still use things like notmuch to index and search on the mbox.
You can migrate messages from mbsync as it provides push or pull, or two-way. You just wouldn't be able to retain a provider-specific email address. That is why I would recommend everyone to use SimpleLogin or similar for email addresses with a custom domain, and then just have them forwarded to whatever email provider you're using at the time.
I'm not exactly sure if you can migrate to a new provider by providing the mailbox yourself, but you can still use things like notmuch to index and search on the mbox.