The biggest feature vBShout has got that MGC doesn't is the ability to create multiple shoutbox instances.
For instance, you can create a separate Shoutbox entirely for your staff, reducing the need for a chat room that may get pushed off the center of attention if the staff member is also part of several other chat rooms.
Other than that, vBShout also has the Active Users sidebar, letting people see at a glance who's active in the shoutbox without needing to load a separate tab.
I can't be entirely sure, but it seems like MGC does not allow users to create their own custom chat rooms and invite people to it - that is a feature of vBShout as well
vBShout also appears to have a more advanced logging system; you can configure vBShout to log all moderator actions and also take a complete backup of every shout as it's inserted (we call it Deep Logging) so that you'll always have a full, contextual list of shouts in case of a dispute between moderators and members.
Additionally, users have extended options for the Shoutbox in vBShout Pro, they can set their individual shoutbox height preferences per-instance, re-order each tab / chat room they are a member of, override other users' font choices, disable display features like alternating shout backgrounds & avatars, as well as configuring global sound options for themselves.
Beyond those features, the two chatboxes have different "feels" - you might want to try the Lite version of each on your forum and see which one your members respond the best to
