Microsoft
You have to understand the pros and cons for both scenarios. Below I'll try to provide few of them (might be others, as well):
Shared Mailbox:
Pros:
- The content of the mailbox can be used at any certain point in time, directly, from clients like Outlook/OWA;
- The mail-flow is still functional. So, in case you still want to receive or send emails from this MBX, you can do it;
- If the MBX is not bigger than 50 GB in size, if you do not have an Archive mbx attached to it, and you do not need to use Hold related features on it, no Exchange Online licenses need to be assigned to it.
Cons:
- If the Primary MBX has more than 50 GB in size, if it has an Archive attached to it or if you want to benefit of the Hold features, a proper license has to be assigned to it;
- The MBX might still be visible in GAL
Inactive Mailbox:
Pros:
- The mail-flow to this MBX will not work anymore;
- Doesn't matter the size of the mailbox, or if it had an Archive MBX attached to it, or not (properly licensed at the time the MBX was moved into the Inactive state), the entire content (Primary MBX, Archive MBX, AUXArchives) will be retained until the time the hold will expire, without a need to have a license assigned (this is something that may change in the future, but, at this time, there is no cost attached to an Inactive mailbox).
Cons:
- The content of the mailbox is available only through eDiscovery searches;
