Having the second dinner makes it easier to participate in a lot of the activities scheduled between the two dinner seatings. You just need to show up at your restaurant at the start of dinner. You have a guaranteed seat in the restaurant. Those with the earlier dinner need to get to the theater a bit earlier to get seats they want for the show.
As far as the activities, there is usually some type of game type show in one of the venues, or maybe a quick change for the kids to ride the AquaDuck. It could also be a good time to check out activities on deck. One of the bars may have live entertainment (which the kids can generally also participate). In the atrium will be some meet and greets (you don't need to buy the photo). And there could even be an activity in the kids club that they want to attend.
As you noted, there is no reason to show up to dinner early, as you will just be waiting outside the restaurant. If nothing else, use that time to walk around the ship.