When comparing CDM vs GDM, the Slant community recommends CDM for most people. In the question“What is the best Linux Display Manager?” CDM is ranked 3rd while GDM is ranked 8th.
Ranked in these QuestionsQuestion Ranking
Pros
Pro Has almost no dependencies
Pro Supports virtually any DE/WM
Pro Very lightweight
Takes up almost no system resources.
Pro It just works
GDM is dull, but it just works, and it is highly stable. It's easy to switch between environments, and it integrates really well with Fedora or other Gnome Distros.
Pro Can run Wayland sessions
GDM can start Wayland sessions, which is the default for recent GNOME versions.
Pro Always signs the GNOME keyring
Works with any desktop. SOome display managers such as SDDM don't open the GNOME keyring at login.
Pro Not so difficult to customize
You just have to know which files to edit, and you can do quite a lot.
Cons
Con Bad documentation & install guidance
Con Bad availability in distros
There is no CDM in distros repositories (only in AUR on arch)
However you always can compile it from source.
Con Curses-like interface
Very simple and minimalistic graphical interface.
Con Tied to Gnome
You basically have to use Gnome or one of its forks to use it properly.
Con Really hard to customize
You'll have to recompile Gnome's resource files in order just to change the login background.
Con Depends on GTK and its dependencies
Con Ugly UI
It is very simple, and you can't change the layout.
Con Bloated
As with anything Gnome, there's a level of inelegance to be expected when it comes to absolute performance. It's supposed to be a login manager, not something bespoke.