Dave Meltzer provided a little more insight into what each man is actually doing, in this week's edition of the Wrestling Observer Newsletter.
According to Meltzer, Heyman and Bischoff each report directly to Vince McMahon, and are "accountable to the entire brand’s interaction with all of the other departments in the company." This entails, aside from the expected creative capacities, being in charge of their brand's merchandise, as well as media publicity.
Veteran WWE writer Ed Koskey remains Raw's lead writer, but Meltzer claims that Heyman has control over the actual direction of the show (with deference to McMahon's oversight).
Meltzer also adds that the pair's positions are comparable to being Executive Vice Presidents, and that, "They are positioned higher than anyone previously in regard to running Raw and Smackdown and are considered major executives in the company responsible for brand management of the respective brands."