Large
A little more formal than big
Large is usually used with words referring to statistics and measurements, such as quantity, number, amount, increase, and proportion.
A large number
Large-scale
Small-scale
We use these expressions to refer to the size of an operation; for example, “The factory began large-scale production of automotive parts.”
Big
There are a number of collocations in which we must use “big” and we cannot use “large”. These include situations and events, for example: a big accomplishment, a big decision, a big disappointment, a big failure, a big improvement, a big mistake, and a big surprise.