Under the Carnival umbrella, I've sailed Carnival, Princess, and Costa. They also have Cunard, Holland America, P&O, Seaborne, and Aida. If you get a low price on any of these, I would not expect much, based on recent expense.with the three I've sailed. So since we are talking BTD, skip these, except maybe Seaborne, but no experience.
Under the RCL umbrella, I've sailed Royal only. They also have Celebrity and Silversea. I've sailed Azamara, but after the RCL divestiture. Royal seemed a little better than the Carnival clan, but not much better. BTD would be on Silversea, but no experience.
Then there's NCL. My experience with them is quite stale, but left a bad taste on a Hawaiian cruise. Their fancy brand is Oceania. It seems like the Oceania thing is more of a pricing thing...more things automatically included. But probably still low-brow basics.
I wouldn't try to go fancy on any of these cruise lines. By that, I mean I wouldn't spend extra to get access to special lounges and pools, etc, and I would not go on their fancy, small ships. The reason is that the same protocols and provisioning are probably ubiquitous, and so as much as they try to differentiate, it's going to be mostly the same.
MSC is separate, my last cruise, and like Carnival, never again. These megas, with cheap nightly rates nickel and dime the heck out of you, making it quite annoying at times. On MSC, the first night after dinner in the hallway outside the main dining room they had a guy pitching the $55 per person per night specialty restaurant! It was a confirmation that they knew the included food and service was sub-par. MSC is not a BTD option.
I've sailed Virgin and Viking (river only) and they are separate from the conglomerates. Virgin was different in a lot of ways, better in many ways, and a few annoying things they didn't do as well as the megacorp brands.