Published figures are rare, but Google has them, and they are stricter than people expect. Gmail caps IMAP sync with two daily thresholds per account: 2500 MB of download and only 500 MB of upload. Hit one and access is suspended — usually for an hour, at worst for a day.
That leads somewhere non-obvious: moving out of Gmail runs about five times faster than moving into it. A ten-gigabyte mailbox leaves Gmail in four days and arrives in Gmail in three weeks, and nothing can change that except planning for it.
Microsoft does not publish its Exchange Online thresholds, so quoting a number would be inventing one. Two migration limits are documented though: messages over 35 MB are not migrated, and neither are folders with a forward slash in the name. Apple publishes no IMAP session limits either; the documented figure is a 20 MB message size cap.
The practical takeaway: a five-gigabyte mailbox usually moves overnight, a fifty-gigabyte one takes a few days, and that is normal. The bad outcome is not slow — it is stopping halfway with no idea what made it across.