And it's a "bananas to hedgehogs" comparison anyway.
For example, K9 doesn't do anything to keep push (IMAP) connections alive -- so if your network provider is too happy about disconnecting them, or the WiFi router is -- K9 will think it's still running in push mode, even though the connection's gone dead.
Aqua sends a dummy keep-alive command every few minutes, so that's extra traffic (although very little).
On the other hand, if you use a Gmail account, try refreshing it from the account list, and when it's done, do it again.
You should see that Aqua is very efficient when there are no changes (no new or deleted messages, no read/unread changes), detecting it in the whole account at once.