The second/third week in June is among the most crowded time of the Summer; school is out and it's when families want to travel. So if you're looking for the time with the most teens, that will certainly do it. It'll also be one of the more expensive times of the year to cruise because of the demand.
We were on the Allure and it's definitely full of amenities and things to do to keep everyone busy and happy. We were crazy about the food in the MDR; tough to feed 6500 people in a 3-hour period and maintain a high standard of quality. While it wasn't bad, we just found it okay at best. The specialty restaurants were very good.
Didn't find it overly crowded most of the times, depending on what we wanted to do and when.
But if you're thinking of doing the Oasis, then you also need to think about the Allure, since they are basically the exact same ship and do the exact same itineraries.