When comparing LXDM vs XDM, the Slant community recommends XDM for most people. In the question“What is the best Linux Display Manager?” XDM is ranked 4th while LXDM is ranked 9th. The most important reason people chose XDM is:
It's a lot more lightweight than the most common GTK or QT based login managers.
Ranked in these QuestionsQuestion Ranking
Pros
Pro Fast and fluent
Pro Works with Nvidia
Works well with Nvidia.
Pro Only two dependencies
Only needs GTK and Xorg-Server.
Pro GTK2 and GTK3 versions
Pro Works well on USB
A full install of arch on live USB works well on many computers with no text issues with LXDM.
Pro Lightweight and fast
It's a lot more lightweight than the most common GTK or QT based login managers.
Pro Allows several seats
Pro Matured Software
XDM is not new, it has been in development since the 80s and is a very stable
reliable DM.
Pro Flexibility
Very customizable and portable, although with not as advanced effects.
Cons
Con Requires Xorg-server
Currently LXDM does not support wayland.
Con Depends on GTK and its dependencies
Con By deault you can't choose desktop environments
by default you can't choose your sessions/desktops, however there are plenty of tutorials on the web to add a selection.