Part of what makes SMB3 so good are the powerups. I don't think a Mario game has captured power ups as good as SMB3 has. The first time you get hammer suit, tanuki suit, frog suit, etc, it feels amazing. It's such a radical departure from just getting a fire flower. Most importantly, they are rare enough that you feel they are really special when you get them. You feel really bad when you lose them, like you might never get it again until the next playthrough.
World was good, it didn't have as many power ups, but having Yoshi was a cool new thing.
After that, the 2d marios got way too generous with power ups. NSMB games just throw the new powerups at you. When playing SMB3, you get a new powerup and you feel like you just discovered something amazing. When I was playing NSMBU, I expected the new powerup to show up most of the time, and it didn't feel that special.
SMB3 and SMW all have very well designed levels, they're a lot of fun and pretty varied. But the power ups are what really makes the games fun and great. I don't think SMB3 would be nearly as well remembered if it only had starman, mushroom, and fireflowers.
NSMB ended up so disliked because it didn't do enough new things. I felt like the levels were well designed, but a large part of the fun of Mario is the skinner's box of hitting those blocks. Finding a 1-up or a really cool powerup feels good. And you didn't get much on NSMB.
And Odyssey, while this is going off topic, is the worst with this. Coins are just there to farm, you never get anything besides coins from blocks. It's boring, it completely removes the powerup and skinner box of opening up question blocks from the game.
Granted SM64 didn't have it either, but I think at that time they did such a good job making small, interesting worlds that people didn't care that much. Not to mention caps were similar to powerups in SMB3, rare enough to feel special but not so rare you can miss them entirely.