Straining the definition a little less than Alexander, some of the First LEGO League challenges came in boxes with the mat folded, making the box unexceptional, but some came in boxes with the mat rolled up.
According to bricklink the 2015 challenge came in a box that was 117 cm long. That is quite a bit more than any of the dimensions of the Millenium Falcon, which according to bricklink came in a box that was 54 x 45 x 39 cm. As I haven't seen other boxes that thick I'm going to guess that takes the price according to volume. (possibly discounting the furniture).
Another regular set that has a large box is 71043 Hogwarts Castle, according to bricklink that box is 58.5 x 48.5 x 18.5 cm, that is a larger front then the Millenium Falcon, but under half the thickness.
I also believe the Millenium Falcon wins on weight, if that is what you meant by size, and can come in a "trolly box":