Agenda, structure and status report is not the way I usually see 1:1 being talked about. Contrast with Horowitz's [1]: "The key to a good one-on-one meeting is the understanding that it is the employee’s meeting rather than the manager’s meeting. This is the free-form meeting for all the pressing issues, brilliant ideas and chronic frustrations that do not fit neatly into status reports, email and other less personal and intimate mechanisms."
Not saying there's not a time and place for Ryan's style.
Well Ryan's meetings are every 2 weeks, that's probably too often for the no-agenda check-in you're talking about. Calling them both 1on1's is the real confusion here.
A friend turned me on to the Manager Tools podcast[1] which is pretty good. They make 1:1s one of the key parts of their philosophy and have some info online about how they do it[2] including the email that sets it up and a sample checklist form for doing it.
I've done these at two different companies both with a team that I grew entirely myself and had already established friendships with before starting the 1:1s and with folks at a new job where I inherited the team. In both cases they were immensely successful in building rapport, establishing a professional-vs-personal relationship, and getting me in touch with how folks are feeling about their work & company. "How was your week?" or "You looked pretty stressed out about the latest feature requests. Everything ok?" works wonders to get people to open up.
Not saying there's not a time and place for Ryan's style.
1 - http://bhorowitz.com/2012/08/30/one-on-one/
1' - http://www.randsinrepose.com/archives/2010/09/22/the_update_...