Both plugins are no longer maintained, which is something important to take into account.
The Ajax Chat plugin integrates the Ajax Chat library, which is no longer maintained. The Chat Room plugin has been built from scratch.
The Ajax Chat library is considerably more feature rich than the homemade Chat Room plugin. Just for you to compare here are some screenshots:
I'm sure you'll eventually face issues with both of them. Worst-case scenario you'll have to ask for help, so I wouldn't say it is a big deal.