Which is the difference between IMA (B777) and Open IMA (A380)?
The primary difference is that the B777 is the AIMS (airplane information management system).  It is a Honeywell developed system where all the software on the systems is controlled by Honeywell (closed system).  The biggest downside to the closed system is maintenance and support.

The A380 system is a semi-open IMA system. It has a single supplier hardware cabinet with processor slices and an common operating system.  Different suppliers can develop their applications to run on the platform.   

Most newer aircraft designs use the IMA architecture as it reduces the number of LRUs and saves weight.  Boeing and Airbus are going to more open systems.  B787 and B777X are open as is the A350, mainly for competition reasons.  Smaller aircraft (Bombardier, Embraer) are typically closed as they tend to have single source avionics (Rockwell Collins, Honeywell).