I know the OP didn't expressly mention it, but it would be interesting to add MSC Yacht Club in this discussion if anyone has done all three.
We've not done
DCL concierge or the Haven, but we did do MSC YC this summer. We have done 2 DCL non-concierge cruises. I can give you our one-sided run down.
We were on MSC Splendida, 2 adults, 2 17 yo dds, 14 yo dd, 11yo ds. We had 2 verandah cabins. We put the teen girls in one and ds with us. We did an Eastern Med cruise - Marseille, Genoa, Civitiveccia, Palermo, Sardinia, Mallorca, Valencia. We found a great deal on rooms and YC cost us about half of what DCL non-concierge verandah would have cost. Our YC was 3 decks in the front of the ship, enclosed, with no way for anyone else to pass through or get in without key card access.
Rooms - very nice, walk-in closet, single bathroom, larger than standard verandah room on DCL
Dining - a dedicated restaurant, service was very European (read slower - they assume you will take hours to eat), food was mostly very good, some misses. It is on the opposite side of the ship from the YC on Splendida.
Butler - didn't really use ours. He was very nice, we're just low maintenance. We did get fresh fruit every day in the room. We could pick which paper we wanted "delivered" to our room (a photo copy of that day's paper.) I picked a major US city paper, forget which one, but actually got a variety of English papers, mostly the Daily News. It became more a joke than an annoyance.
Pool - large private pool area, rarely full, with bar, that served warm breakfast and lunch also.
Lounge - the best part of YC, hands down. Large, rarely full, at the bow of the ship with incredible views, appetizers out what seemed like 24/7, bar, helpful staff. A calm oasis, where we spent a lot of time playing board games or the kids set up their Nintendo Switch, making many international friends.
Concierge desk - helpful with our several small details (getting "parent" cards for the opposite rooms, etc.) They also provide an escort off the ship each day to jump the line getting off, and had staff on the pier to escort you in the same fashion when you reboarded.
"Extras" - dd got a stomach bug for a day. The dining room gladly delivered chicken broth and mashed potatoes to the room for her.
Escort/reserved seats at shows - not sure this is needed, but we're not big show people. The few I went to were not full. My dad went to all of them and said several were very good.
The downside was the rest of the ship. I much preferred the Wonder/Magic, or our Oceania cruise ship Marina. It was crowded outside the YC, the layout forced you to walk through numerous bars/lounges to get anywhere. There were many pools, which is good for pool folks.
On a port intensive cruise, and for the amazing price we got, this was fine for us. MSC sells the YC as "a ship within a ship" and that's what it feels like.