Which do you use and why? Does one provide any clear advantages over the other?
4 Answers
I use admin_menu for administrators and developers who need quick access to administration functions, but I use admin for everyone else.
Admin's main weakness for administrators, that it only shows you one section of the menu at a time, is also its main strength for content creators and maintainers who would be overwhelmed by all menu options. The fact that you can have a sidebar with just Create content is great for data entry.
A big plus of admin is its ability to be tucked away into one corner instead of taking up the entire top of the website. In my user testing, people don't seem to think they're editing the live site when the site has a toolbar attached to it: before switching to admin, I would frequently get questions asking how they could see the live site when logged in.
Be careful using admin menu, for sites with lots of modules it's buggy, in my experience. It disappears without reason. I've been developing websites on Drupal for 5 or more years and admin_menu was one of my favourites admin tools... For small sites, I recommend it. For sites with lots of modules I wouldn't recommend it. See the admin_menu isssues, search "disappear" and you will find people complaining about it. Some patches have been submitted, in my case the bug persists. Be careful with this module on D7.