The difference looks like this:
They also connect to the torso differently. The Heavy Intercessor one has a line running around the other side that slots into the torso instead of the classic peg and hole system of Marine backpacks.
The Heavy Intercessor backpack has greater thickness, too. The central part is like the normal one, but thicker by about the depth of the round thingy in the middle of the regular Intercessor backpack, and then has its own round thingy mounted on top of that.