Overall, I do think the Pro's have it. It is lovely to be part of a community that reads and Bookclubs are a great way of finding that community. However, in this online world, many bookclubs take the form of online discussions of assigned books each month.
The issue with that for me is that who ever is setting the books will probably have an agenda. If it's coming from a book shop or a TV show, the choice of books is completely determined by the publicity departments of publishing houses. You as a reader get very little say as to what you all read next. In contrast, by joining in with reading books in the Richard and Judy book club, Oprah's or something with Waterstones, you are probably going to be reading the most recent titles, the ones that everyone is talking about.
For many people the attraction is getting out of the house, but as libraries and physical meetings are in decline there's so much more available online. There is something I do not love about the online style of people sharing their ideas by writing what they thought, no one can type fast enough to keep up with an interactive chat!
We have a book club at work where a different person decides the book each month and we meet at lunch time for a drink and a chat about the book. It's brilliant, people bring their own thoughts and questions and we really get to tear things apart, things that others didn't notice etc.
My advice would be to definitely find a bookclub that meets in person and find out what the decision making process for the next book is.