Big atty's (XL/MEGA) are for using the big carts. There are two types of big atty's and carts. There is a model of big atty/cart in the line of 510 that can be used in the eGo/Tornado. This is twice the size of a standard cart for a 510. Besides, there is another model of big atty/cart that is specific for eGo/Tornado and can hold up to 2.5 ml of juice. These are the only differences with the standard atty/cart.
As for LR, the main benefit is that you get warmer vapor, thus stronger throat hit and more smoke sensation. The bad side is that they consume more juice, so if you try with cartridges you need a fast-wicking mod for sure.