Super Mario 3:

More levels (I forget the exact number, but it's something like 110-120 levels, versus 96 exits out of 60-70 levels in World)
More items (Tanooki, Frog, Hammer suits, music boxes, clouds, p-wings, etc.)
Kuribo's Shoe (is just awesome, see avatar :D)
Awesome secrets (white mushroom houses, coin ships, etc.)
Better Bowser battle (purely IMO, but I think the Bowser battle in Mario 3 was much more epic than World)

Super Mario World:

Bigger levels
Yoshi (he is pretty awesome)
Better graphics/sound
Save game feature

I vote for Mario 3.  More levels, more items, more secrets... the key word here being more.  It was just more game.  I also thought the themed levels were much cooler in Mario 3.  Desert land, water land, giant land, sky land, ice land... Mario World didn't really do this too much... and the first time I got to giant land was pretty epic.  The biggest flaw with Mario 3 is that, for such an epic game, you really need a save-game feature. 

The master himself (Miyamoto) has stated that Mario World wasn't all it could have been, bringing very little new to the table over Mario 3.

In the end they're both awesome games, but my vote goes to #3.

Even though I think the level design is superior in SMB3, my vote goes to Super Mario World because of Yoshi, the ability to save and the fact I have lots of nostalgia for it.

Without a doubt SMB3 (Which I consider the greatest game ever made). Nothing against SMW, I love it as well, but SMB3 completely changed what Mario could be and from the age of 5 onward it's made a major impact on me.

Yes, without a doubt SMB3.

Super Mario Bros. 3 is my best game ever!

Super Mario World

Yoshi is an amazing power-up, and the ability to go back and play any previous level at anytime is a great feature.  That feature was added to the GBA version of SMB 3, but it is only available once you beat the game.

Super Mario World. Best music. Yoshi. Awesome sprite art. 

It was also my first game I ever played :P

I'm gonna hafta go with Super Mario World on this one. Yoshi was one of the best video game power ups ever (and baby Yoshi is just adorable) and the music is out of this world. Dinosaur Land was a great place to visit for sure. ^_^

Oh, and saving was nice too.

Hm, I've only played Super Mario World, haven't gotten very far, maybe like halfway through. I love 2D Mario platformers, but I suck at them. I think NSMBWii is really fun, but I'm not very good at it. I've heard that SMB 3 is like the best one ever, but I haven't played it yet. I will soon.

Wrong.

Wrong wrong wrong.

The number of secrets in SMW is mind-boggling compared to SMB3.

OT:

I don't like SMB3 at all and love SMW, so SMW.