I don't think this is Mail.dll problem, especially if Gmail is several times faster.
On my machine (located in Europe) whole sequence:
- Connect using SSL/TLS,
- Login,
- Close and disconnect
takes 1.3 - 2.1 seconds for Gmail,
and 1.5 - 2.8 seconds for Outlook.com.
and 1.6 - 2.8 seconds for Office365 (pod51009).
My question is what takes most time: ConnectSSL or UseBestLogin?
There is also a good chance that email provider is slowing you down on purpose (you send too many emails for example).