Large, big, great mean above the average of its kind in magnitude, especially physical magnitude.
Large may be preferred when the dimensions, or extent, or capacity, or quantity, or amount is being considered.
Big, on the other hand, is especially appropriate when the emphasis is on bulk, or mass, or weight, or volume.
As applied to material objects, great has been practically displaced by large or big. Where great is used to denote physical magnitude, it now regularly connotes some impression (as of wonder, surprise, amusement, or annoyance) associated with the size.
Great alone, in standard English, expresses degree. In extended use, great suggests eminence, distinction, or supremacy while large suggests breadth, comprehensiveness, or generosity and big carries over the implication of mass or bulk but often suggests impressiveness or importance rather than solidity or great worth.