What are the pros and cons of Chat vs Private Message

Hello,

I'm examining both of these plugins and would like to know when, why and what criteria that I need to consider in choosing Chat vs Private Message plugin.

They both look great, but have some overlapping functions and usage.

What are the strong points and weak points for each one?

Can I run both of them on the same site? Is there a point in doing so?

I appreciate your in depth analysis on the merits of each of the plugins versus the other, and the use-case scenario for the best fit for each one.

Best Regards.