Just wondering if I'm missing out by not joining that group.

Thanks,
Roger

Some people belong to both, others prefer one or the other.
On LDO's message board you do not have to give your real name, which can be a benefit if you do not want to share your information about becoming a donor. We also moderate these pages. The messages here are organized in a way that you can find topics easily, and you can search for topics or keywords.
On facebook you would be using your name, and that's fine if it is not a problem for people. Users have to abide by facebook rules and guidelines. Each topic thread gets pushed down as newer posts are made, and searching the group for topics is not an option.

Another thing to think about is how public your participation is with your real name on Facebook.  Concerns about that have led to our have two groups there:

The older one, with more than 1,000 members, mistakenly changed to "Secret" privacy, is at https://www.facebook.com/groups/LivingDonorsOnline/.

The newer one, likely to be the one you're looking for, with "Closed" privacy, is at https://www.facebook.com/groups/livingorgandonors/.