Overall, the New Super Mario series was a huge step down from the SNES's Super Mario World (SMW). Instead of giving us more of what made that game great, they carved up those things and fed some of them back to us over the next 20 years in pieces. Some of the best elements like the cape and being able to bring Yoshi between levels never made a return, while others took multiple entries in the series to come back.
New Super Mario Bros (NSMB) for the DS was a massive step down from Super Mario World on the SNES. They removed most of Martio's moves, all flight powers (especially the cape), removed Yoshi, and messed with the physics. The point of the game at the time was to "recapture the magic of the original SMB", which meant back to basics. It's my least favorite 2D Mario. I was playing SMW rom hacks, so I wasn't starved for content like everyone else was to put up with how much worse it was than SMW and SMB3.
New Super Mario Bros Wii (NSMBW) added the 4-player co-op, which was an advancement, and I had a lot of good times playing it with friends. They started slowly adding SMW elements back in with this one. The spinny cap was a weak flight power, and Yoshi was back for a few levels. The music was bad enough I made my own rom hack to replace it though. The spin made up for some of the inconsistancies in the physics, even though it made it easier.
NSMB2's big gimmick was coins, which was kinda dumb. Co-op was still pretty good, but you needed two 3DSs and two copies of the game. They added in the racoon power, which was Mario's second best flight power. Nintendo was (and still is) too cowardly to give us the cape back though. I ignored this one for a while, but ended up having more fun with it than I expected. Still pretty forgettable.
NSMB Wii U gave us back the world map from SMW as well as multi-color Yoshi's that you can bring between levels. However only baby Yoshi's and they were much harder to get and keep. It's got similar co-op to NSMBW and plays in HD, but otherwise is quite forgettable. The ability for the second player to assist by using the game pad's touch screen was neat and let non-gamers play too. But that was lost in the Switch version.
Mario Wonder - This game is a departure from the "New" series and actually feels unique and memorable as a result. It's my favorite 2D Mario game after SMW and this game just oozes charm. The animations, how enemies react to you, the soundtrack that adapts to what you are doing, the detailed backgrounds; overall the world just feels so vibrant and alive. The Wonder flowers add a new gimmick to every level and they are hugely varied and tons of fun. The co-op is massivly improved with less getting in each other's way. It finally brings back Yoshi, but with the second player controling it. But that's actually perfect since it allows players with less skill to either ride the Yoshi or to be the Yoshi and get the flutter jump from the Yoshi games and infinite health. It's also got a world map that is arguably more interesting than the one in SMW. Even if the NSMB series turned you off to 2D Mario, you need to play this one.
Honerable mention: Mario Maker. The Mario Maker series lets you make custom Mario levels and play levels other people have created. But it also comes with 50+ levels made by Nintendo, which are actually really good. Since the level can be made in the style of other Mario games, it finally brings back the full move lists of SMW and SMB3, even if you can't keep powers between levels. The levels are all unique between the Wii U, 3DS and Switch games, making all three worth a playthrough. The Switch Mario Maker was my 2nd favorite 2D Mario up until Wonder, and it adds elements from Mario 3D World, an excellent story mode, and even world maps if you have Ninendo Online. It's actually the only reason why I have Nintendo online. Still, I enjoy playing a good SMW rom hack over the random levels and worlds online.