Blanco is correct in how infoshare works. Basically, if you have two groups near each other, and group A sees the enemy (but group B normally does not), then infoshare will make group B also aware of those enemies. In the same situation with groupchain, group A would see the enemies and go into "combat" mode. Group B would then be put into "combat" mode as well, but would not know about the enemies group A knows about.
In many situations like the above, the result of both scripts would look the same, although with infoshare the AI would most likely start firing back at the enemies sooner. However, there are many situations where infoshare would do nothing, while groupchain would do something. Whenever a unit gets injured, groupchain will kick in; whereas infoshare only kicks in when actual enemy units are spotted.
So the AI would react to camcreated artillery, mines/satchel charges, or sniping without being seen exactly the same under infoshare as it would with no script running at all: the group that gets hit would start running around like the sky was falling, while all their friends in other groups around them would continue their business like nothing was happening. With groupchain, every group that is "linked" together would react to the above situations (instead of just the group that got hit).
I hope that clarifies the difference between the two scripts. The visible result of both scripts overlaps in some ways, but in other ways they are different. Running them together shouldn't cause any problems at all (since they work in different ways internally), and in fact would likely make a mission much better than just running one or the other individually.