i've been on both liberty of the seas and norwegian gem (sister ship to jade, so very similar). liberty was far and away the better cruise and ship. for perspective, i've been on liberty 3 times and am going on her again this summer; i went on gem once and have not been back to norwegian.
i find royal fairly similar to disney, but for me the gem felt like a definite step down - horrible MDR food (ok in the specialty restaurants, which we went to after the third night of inedible MDR food, but i didnt appreciate having to pay for dinner to get an edible meal for the rest of the week), horrible entertainment and not a lot of activities for adults unless you drink a lot (which you mentioned you like to do, so maybe that wouldn't be an issue for you
), cheap furnishings (instead of a couch in the room there was a futon-like thing in our balcony cabin), and the worst service we've ever had on a cruise.
i'm sure there are norwegian fans on here who will disagree.
but, if you're used to disney, i can't imagine going on norwegian and not being kind of bummed, unless you really adjust your expectations downward.
i don't have kids so can't speak to that directly, but my friends with kids/teens have been really pleased with royal's programs. liberty also has a rock-climbing wall, mini-golf, and flowrider (surfing simulator) which are good for the teen/tween age group. i don't recall the gem having anything like that. i'd check out the norwegian board on cruise critic, as people have been complaining about cuts to the kids' programs there, but i don't know if that covers the teen programs, too. keep in mind that unlike disney, royal charges for the kids' programs at night - again, i'm not sure that that covers the teen ones, but i believe so. i don't know if norwegian does.