Every integration method has its advantages and disadvantages, and its really hard to propose one based only on what you have provided, but here is some hints:
- Quick and Easy: if you don't mind high coupling, and major changes in the applications are not expected (like DB engine, or replacing on with non-Java system), you can go with RMI or even DB Procedure calls.
- Changes, Extendability and Scalability: if the applications are expected to be changing more than rarely -and they tend to do-, ESBs or Message Queues would be great, since they would produce a loosely coupled architecture. This would also make room for extendability (like if you would have a new application C, that would need to invoke A or/and B)
- HTTP Availability: If HTTP communication is available between applications, Web Services is an excellent integration method.
- Developers Knowledge: What technologies you/the team are familiar with.
These are actually small hints, if you wish to go further in your research, I strongly recommend reading Enterprise Integration Patterns the book.