Mongoose, under the auspices of Issaries, will be using much of the BRP system. There are reportedly some substantial changes in combat, and magic has yet to be seen. Chaosium is not involved with this project.
Greg announced that Mongoose would be able to use the BRP mechanics by re-stating them in new words. This allows them to use the system without the permission of Chaosium, since game mechanics can't be copyrighted - only the specific text used to explain them.
So there will be two new RQ-related systems out there. One will be Chaosium's new multi-genre Deluxe Basic Roleplaying, which may be given a new name. The other will be Mongoose/Issaries' new "RuneQuest", which will feature Glorantha and other settings.
Which of these two systems will be closer to RQIII, and what the effect will be of these systems on each other, remains to be seen.