I have sailed on NCL with and without kids and Celebrity with and without kids and several other lines with and without as well. My family has enjoyed them all and my wife and I have enjoyed them all without the kids, too.
Having said that, if your kids are active and would enjoy waterslides, video arcades, etc., then NCL would be a great choice and yes, there are still plenty of areas where you can read a book. Our family prefers NCL to either Carnival or Royal Caribbean for whatever reason but for families and kids those three are more similar than different. The shows and entertainment on NCL are typically very good and I think the main dining room food is better on Carnival but is worse on Royal Caribbean, NCL being in-between and perfectly fine. NCL has the better buffet of those three.
Everyone will have a different opinion here but that's been my experience. On any of the newer NCL ships you will be able to have a great family cruise, and that obviously includes the Escape.