Royal Caribbean is great for kids, but we also love NCL. We tend to find they've got the most bang for your buck (especially if you want to drink on the cruise - the drinks package on Royal Caribbean is eye wateringly expensive).
We also like the freestyle element of NCL - no formal nights, eat where you want, when you want, no need to sit with strangers or at a set time each evening. You just turn up to the restaurant, you either get seated straight away, or they'll give you a buzzer. We've never had to wait more than a few minutes.
We've taken our three teens on cruises on NCL, and there's been plenty for them to do. Check out individual ships, as not all have a sport court, but we went on the Norwegian Getaway, which had a sports court and water slides, swimming pool, hot tubs plus table tennis, ropes course, giant chess, bowling, arcade, and shuffleboard (surprising, my DD's favourite thing to do!). Some ships also have karting or laser tag, but this tends to replace a sports court.
My middle son spent his whole time playing basketball and football with other teens, and none of them went to the teen club at all. But it can be worth going to the teen club on the first night, just to make some friends, then making their own arrangements after that.