What are the major differences in between the flying of, say, a drone like the Predator, versus the QF-16? What changes so drastically in the handling of the aircraft for the remote pilot? Are the increased maximum speed and loading the only thing that makes this flight different?
USAF has been flying combat aircraft converted into target drones for decades; calling it the next big step is a few decades too late. The best possible explanation would be that the buzz was created in context of the armed UAVs being used in combat operations.
In the strictest sense, the differences in the two platforms are the same as the aircraft they are based on. QF-16 is based on a combat aircraft and as such brings to the table advantages like maneuverability, speed etc and corresponding limitations. On the other hand, the Predator (MQ-1) is based on a reconnaissance platform and brings the advantages like endurance, quietness etc. while limited by payload and speed. The handling qualities vary accordingly.
Another dimension is the use of experience gained in designing/operating QF-16 in the development of next generation combat aircraft which are expected to be optionally piloted (for e.g. the preflight tests on QF-16 are carried out by a pilot, who then exits the aircraft).
Another consideration in the difference might be latency as discussed in this question. I'm just guessing that a target drone would be flown from somewhere near the location of the exercise. As opposed to half a world away like the predator.