Generally speaking, larger saws are usually those used for more rapid and aggressive cutting.
Hand saws for wood, bow saws and two person saws, are all examples of larger saws designed for cutting quickly through materials.
However, larger saws usually have fewer teeth per inch, and so speed and efficiency comes at the expense of a rough finish.
Smaller saws
Smaller saws sacrifice speed for a neater more controlled cutting action.
Coping saws, hack saws and compass saws are all examples of smaller saws, and are used for making shorter, or more complex cuts (such as cutting out intricate shapes).
Their smaller blade means a lighter tool which is much easier to manoeuvre.