My situation is a bit different as a family of 4. I understand that what applies to me may not apply to others. My MSC experience is only with Seaside but I have Meraviglia and Seashore booked.
On NCL, there are many more options for 4 in the Haven than in the Yacht Club. Using Breakaway, Getaway, or Escape, there is the Deluxe Owner's Suite, the Owner's Suite, the 2BR Family Villa, the Forward-Facing Penthouse, and the Aft-Facing Penthouse for 4. On Bliss, Encore, and Joy, the options are mostly the same (no Owner's Suite) but now, Joy has even more (former Concierge Suites turned into Haven Suites).
On MSC, the choices are much more limited. There are fewer stateroom types to choose from and since parties of 2 and 4 are fighting for the same staterooms, it's harder to get exactly what you want. I was forced to take the Royal Suite on Meraviglia because that was the only stateroom that was available. I booked before the Duplex Suites were converted to Yacht Club and I even considered switching but by that time, the price had risen to the point that it wasn't worth it. Even though neither stateroom has a great balcony view and both have a whirlpool on the balcony, I decided to stay where I was and keep the one bathroom vs. having two in the Duplex.
I think I prefer the forward facing lounge on Seaside vs the BA Plus ships because you can walk outside from the lounge on Seaside.
For forward-facing sundeck, some of NCL's (BA/GA/Escape) are rather small for the Haven. On some ships, the entire forward-facing sundeck is Haven and NCL might expand the Haven sundeck in some cases but on Getaway (for ex.) they kept the small Haven sundeck and expanded VIBE's area to include the larger front-facing area and port side in addition to the starboard side that it already had. Personally, I would have expanded the Haven sundeck to include the front section while giving the port side to VIBE (the way that Encore is). Even better would be to split the Haven sundeck into all ages on one side and adult-only on the other side. No real complaints about MSC's sundeck. Some people don't like the lack of shade but it's not a problem for us. The food and drink options by the pool are easily better than NCL.
I think that NCL concierges have more "power" to get things done vs MSC concierges.. On the flip-side, MSC's butler service is much better than NCL's. I've never had a bad butler but I read more complaints about NCL butlers than MSC butlers. Maybe I've just been lucky with both.
In suite dining is much better on NCL. Any meal from nearly any restaurant can be served in suite or on the balcony with NCL. For MSC, the options are very limited in comparison.
Sorry for the long answer but since I enjoy both, I started remembering things that I enjoy about both lines.
Anyway, back to the OP....
Have you looked at "The Retreat" on Celebrity?
It's basically Celebrity's version of the Haven without calling it a "ship within a ship". It started on EDGE and APEX and is being added to some older ships in the fleet.