all4wdw, we have stayed at the Polynesian concierge 3 times. It is great for our family of 5. Our kids are a little younger than yours (6,3 and 1). We had a reservation at the YC concierge last year. We decided to go on a tour to see if we wanted to stay at the Polynesian or keep our reservation at the YC. We decided after taking a tour that we would rather stay at the Polynesian. It wasn't because we didn't like the YC, it was just that the Polynesian was better for our needs. I don't know if your needs are the same but here were some of the reasons:
We spend most of our time at the MK and we have a stroller so it was better for us to have the monorail to take to the MK and Epcot.
I think the Hawaii bldg is the best location at the Polynesian, it is right next to the beach, the pool, the boat and close to the GCH. If we were staying at the YC it would have been a hike to SAB.
I also prefer the lounge in the Hawaii bldg, it's huge and you can't beat the view

The lounge in the YC is small and there is no view.
I also like the simple layout of the Hawaii bldg. The YC has many halls, and I didn't want to have to walk to far to the lounge.
Those were some of the main reasons why we stayed with the Polynesian concierge. Your needs might be different.
Our needs will change once our children are older and we don't need a stroller.
The YC seemed fine for families. I would stay there, but like I said some things were just more convenient for us at the Polynesian.
We are going to give the BC a try this summer. I'm still debating on doing concierge or not?