I could talk about how great Super Mario Bros. 3 is some more. I think I've posted about that game about six times since I got my NES Classic Mini.
You know what a strength of this game is? The levels that are puzzle levels. Stuff like 7-5 or that one World Six level that blocks a house with a Hammer Suit in it. Sooooo good, and a nice change from the platforming-heavy levels.
There is so much variety in this game.
Also, I think one reason that I prefer SMB3 is that since there is no save on the original cart, they had to make the levels short. In turn, I think these levels are more tightly designed and ultimately feel more cleverly laid out than, say, levels in SM3DW or Galaxy 2 (though there were some clever levels in the latter game). Playing a level in Mario 3 is a short burst of frantic platforming or puzzling (or both), and then you get to take a breath and go to the next (and often different in terms of what it will ask you to do) level.
Playing levels in modern linear 3D Mario games seems like it takes forever, and in something like 3DW, most of what you're doing seems trivial since most of the level is wide open since it's meant to allow for effective multiplayer. I don't want to make the comparison to stealth-crap on 3DW (really!), but because that comparison helps me to explain what I love so much about SMB 3.