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Looking at British Passport application timeline, most applications are either post office check and send,
or postal application by applicant himself/herself to apply for their FABP – First Adult British Passport.

Browsing the HM Passport Office website, there is a third way of applying for first adult passport, where in you fill up the form online (so hopefully no mistakes in printing name on passport etc.)
HMPO will send it back to you for signature (I presume plus adding photograph and counter signatory etc.).

I just like to know if anyone used this service for their first adult passport following naturalisation?
Please share your experience if you have.

With the online version there will be some additional delay as one has to wait for the printed application form to be posted out and then one should go about getting references etc... But with the postal mode the application can be filled-out and perhaps even the references obtained prior to the Citizenship ceremony. After the ceremony the certificate number is entered and the application can simple be dropped into a postbox or sent though check and send if so one prefers. As a result the postal route will be quicker is my guess