If a have a partner network that use the same partner portal license and I migrate them to a partner community, will they be able to send each other chatter message in the community or is the chatter message hierarchical and rolls up to the parent org? For example, I have Partner A that has two user logins through partner portal A and Partner B that has three users that login through portal A, then what will their chatter capabilities be if I migrate Partner A and Partner B users to Community A.
Partner Communities licenses have access to the full sharing model, while Customer Communities licenses are limited to sharing groups and sharing sets. What that enables in your scenario, is the ability to make the User object private, and therefore restrict the visibility of partner users and their chatter activity from each other in the same community.
Once you make users private however, you would need to open up user visibility (partners from the same account for example) with sharing rules. The most likely use of sharing rules in a partner community setting will be either criteria-based sharing rules or apex sharing, since each partner gets its own role, role based sharing is impractical. Keep in mind that users will be able to see all groups in the community regardless of user sharing restrictions.
EDIT: I should mention that default setting is for the user object to be public, and partners can see and chatter to each other in a community.