On our first cruise last summer we had to take late seating because early was booked up. We were travelling with a 12 year old and a 17 year old, so their ages didn't matter as much as the fact that we all were used to eating by 6pm. So, we were a little worried. Turned out just fine -- seeing the show before dinner worked out for us as I have read many others say because we had some relaxed time afterwards to get some photos taken, walk on deck, etc. Plus eating later for us didn't seem to matter since all concept of time seems lost while aboard the ship. We never really even felt hungry ever -- with so much eating available constantly.
This summer we asked for early seating when we made our reservations, and again were told it was not available. We just wanted to try it. But to our surprise, upon checking our dining tickets the first day in our stateroom we saw that they gave us early seating! So, we got to try that time as well. We felt that there were some minor advantages to both, as well as a few disadvantages. Early seating had more babies and toddlers at it -- consequently a louder dinner time if you know what I mean. There were young children at late seating also, just not as many. I would say a main disadvantage to early seating is the rush to get ready after a day at Castaway Cay, and the fact that with early seating you get the "joy" of early breakfast on the day of debarkation -- 6:30 am. We actually skipped breakfast in the main dining room this trip because we did not want to go at 6:30am.! We also liked late seating because there was no diners after us, so the waiters weren't trying to rush things along.
If my kids were still toddlers, I would try for the earlier dinner -- just because they are less adaptable to change in dining times than older children.
Either way, we'd be happy to go again tomorrow!