Glad Disney is not over after 12. I had been considering myself "on borrowed time" with each visit, but this brings me hope.
I think it just depends on the kids. IME, with my own kids (16 now, twins), they're kind of like adults going to Disney in that they can have some of the same type fun they had when they were "little" if they want to and not be embarrassed about it or whatever, being among like-minded people. We had a lot of people tell us our kids would "outgrow" Disney, but they haven't, at all, and I don't really expect that they will. DD fell in love with the GF on our last trip and asked about (her) buying DVC and what it means, etc. (I told her to keep her college debt low and maybe she can some day!

) DS keeps park music on his iTunes and listens to it all the time, etc.
Visits do change a bit in that, when they're little, parents make decisions about how to tour and that's the end of it. Little kids go with the flow, so to speak. Not so as they get older. They have their own ideas about things, yet they sometimes have no clue what they're doing. When mine were 9 or so, on one trip, we were over by Frontierland and DS insisted he wanted to go on Splash then and there. We tried to explain it wasn't a good time, that we'd go do something else and come back later when lines were shorter, etc., but he was getting all bent out of shape about it, he wanted to ride it then, lol. Although he'd had many trips, he still didn't get the whole strategy part of it. But he learned and now he'll suggest strategies himself, sometimes ones we may not have even thought of.
One of the biggest upsets with my kids - ever - was on a trip when they were 13. We had our morning planned but plans were thrown off when a ride was down and I forget what it was but something else happened. Anyway, we all had different ideas about what to do next. Next thing I know, in their excitement, the kids ran off to do something by themselves. Remembering our many trips with them in the strollers and us doing things together as a family, etc., it hit me that day very hard that they were growing up and now had different interests than ours, and I started to cry. I mean, to the point where I surprised myself.

(They say we all have our moments with this and this was mine. Fortunately that was the worst of it and it's never happened that severely again.) I'll never forget the kind CM in a gift shop, a fellow mom, who talked me down when she saw me upset.

Later, DH made me laugh when he texted me to come meet them and I found him with the kids jokingly in a double head lock.

(The picture I took of them at that moment sums up a lot of how we as parents feel about them when they're teens! We love them but we want to "strangle" them sometimes.) (*j/k, of course in case anyone takes that literally)
Last trip, at 16, was awesome and we fully expected they'd go off at times on their own. In fact they did all 4 parks on their birthday (while we did 3 with them, with a good mixture of things we did together and things we did separately). We felt comfortable with them getting back to the resort by themselves, even at night and park closing, etc. (They are mature and would not leave eachother's side, were in touch with us by phone, know the areas very well, etc.) It was fun hearing their stories and experiences later, and how they handled problems, arguments (with eachother!) and money, etc. I also heard them talk this trip about what it will be like when they take their own kids to Disney someday, so that was pretty heartwarming knowing how special it's been to them.
I guess you could say it's a process as they grow up...
Good thread!