IMO, the only reason for a big toy box is for big toys. We have a small laundry-basket-sized tub in the living room for toys. Once every couple weeks I sit down with my 3.5 yr old to clean it out b/c all the itty bitty toys go down to the bottom of the tub when he cleans up real quick-like and just tosses it all in there. He's been looking for that marble or that magnet or that small gi-joe gun for the past week, unable to find it b/c his big toys are on top. The only way to get the small ones out is to take ALL the toys out of the tub. NOT FUN for me! It just makes a bigger mess. I try to keep the kid organized within the tub (keeping gijoes in a small bag, magnetic letters in a different clear bag, etc) and keep a tub full of organized bags in there, with some of his toys organized in shoe-box sized tubs in his room.
This is an interesting question though, because one thing I did want to get for my son's room was a "toy" chest, but one that has a flat table-top so that he could have a 'child-sized' tabletop to play on with his blocks, cars, and little people type of toys. I was hoping to find a shallow box, with legs, to put it at his level so he can stand and play. Know what I'm saying? Basically- if you get a toybox, the shallower the better so that they can find stuff, and a flat-top would be better because you could actually play and use the top of it. I have not yet found my 'dream toy box' but my carpenter friend may make me one like this (cedar chest, but take out some of the depth and add legs instead) http://www.johnsonsantiques.com/product_images/4537989894...