We have done both with a family of 5 also. The bed configuration is slightly different in both. In the concierge room, the sofa folds out to a double and there is a single bunk over it. In the non-concierge room, the sofa is a single, there is a bunk, and there is a fold out single that comes down in front of the door to the veranda. Not sure if that makes a difference to you or not. The double sofa in the concierge room folds out so it also blocks the veranda door so there isn't one layout that is better than the other for not blocking the door. However, in concierge it is easy to fold the sofa back in in the morning to free up the space before the stateroom host comes back in. You can't do that with the fold down single bed from the wall.
From a veranda space perspective, in concierge, you can book what are called 'bump out' rooms. They are located in the curved out forward portion of the Dream/Fantasy on deck 11 and 12. We have stayed in 12008, 12010, and 11004. The extra veranda space is fabulous! We asked concierge to bring 2 lounge chairs and an extra regular chair and all 5 of us sat out there at times. The lounge chairs were a great touch too. You can't fit louge chairs in a normal veranda. You have to ask for them though...even the bump outs only come with 2 regular chairs. They are also still completely covered, eventhough they bump out.
Regarding concierge...it spoils you. The separate floor that is just concierge tends to cut down on noise in my opinion. The lounge is great, and ALL the amenities that go with concierge. Being able to book the max number of days out helps a lot. We love the cabanas on CC, so being able to be the first group to make excursion reservations enabled us to get one each time. Even checkin at port is a much better experience because of the separate line, waiting lounge area and early boarding. If you can afford it, it is well worth it to us. We are doing non-conceirge this upcoming weekend in a cat 4 because there are 15 others sailing with us and it we didn't want to do concierge when they weren't....and I know we are going to miss it.
So, besides the slight difference in bed layout and the option of getting a much larger veranda with a bump out in concierge, you don't notice that much of a difference in the family staterooms categories when you are in the rooms. It is the amenities that come along with concierge that make all the difference.
One side note, in May, we were cat v on the Dream on a 4 night. We asked about upgrades and we were able to upgrade for 400.00 TOTAL to a 1 bedroom suite for the 5 of us. That was awesome. We also had stateroom 12000, which is in the very front of the ship and had a giant bump out deck that was HUGE! The extra bathroom, twice the space, a dining room, living room, etc was just great...and you couldn't beat the upgrade price when normally it would have been 3-4,000 more for the 5 of us.