RefPtr in the current stable glibmm family is an intrusive refcounting smart pointer, i.e. it uses GObject refcounting.
In unstable, it is an alias to shared_ptr, so it uses a different layer of C++ refcounting instead of GObject.
As for which is better, I guess the above answers that too.
Btw, neither relates to Gtk::manage(), which is about letting containers manage the lifetime of their children, i.e. restoring the floating reference semantics that widgets have by default in GTK+ but not in gtkmm. RefPtr is not used with widgets.