With the Expression you have more size options. You can make much larger pieces, but also smaller pieces. On the baby bug the smallest setting is one inch....on the Expression, it's a 1/2 inch (I think...I know I've cut stuff at 3/4 inch).
There are features on the Expression that the baby doesn't have. Some of my favorites are auto fill (will cut as many of an item as will fit on the paper without you having to figure out how many will fit), fit to page (will cut the item as big as it can fit on the page), quantity (you tell it how many to cut, push a button, then do something else while it works), and flip (will cut the mirror image of an item).