We've done both lines as well, and I would never pay $12K more for Disney, especially for a group of adults in Europe. Even if you are really looking for the Disney element in your vacation, you're not going to have much time to experience that on a port intensive cruise like Europe.
We love DCL, but had a wonderful cruise on NCL last summer. There were things we missed not sailing on Disney, but also things we preferred on NCL. Personally, I'd pick the itinerary, timing and pricing that worked for our family and not worry about which cruise line we are on. Apart from the Disney aspect, I honestly don't find any big difference between Disney and the other mass market lines.
You didn't say which NCL ship you were looking at, and they have several in Europe, so I did want to point this out. If you are looking at the Epic, check out the bathroom layouts. There really isn't a separate bathroom, per se, but a little toilet area and shower area (both separated from the main part of the cabin by frosted doors) and the sink inside the cabin itself. It doesn't bother some folks, but some hate it. We've never sailed on that ship, so I don't have any first hand experience, just what I've read online. You will only have that issue on the Epic, though. NCL's other ships have regular bathrooms.
We are sailing on the NCL Jade next year in Italy and Greece. I looked at Disney's itineraries, but they didn't have any that compared to the one we are taking and the prices were much, much more than we would want to spend. It's a shame. We were on the first DCL Iceland cruise and it was fantastic. DCL does a wonderful job in Europe, but their prices have just gotten past the point where we see the value anymore for sailings that are more about the destination rather than the ship.
ETA: With as many people in your party as you have, be sure and price out suites vs multiple cabins. You might find that the pricing is better for a large suite vs a bunch of individual cabins. NCL really knows how to treat their suite guests! We've never been able to stomach the cost for DCL concierge, but quite enjoy the NCL suite life.