Big, large, and great can all be used to talk about size. They can all be used in front of count nouns, but only great can be used in front of uncount nouns.

Big is the word you usually use in conversation.

1. Where? — Over there, by that big tree.
2. Ellen had a big bag of eggs.

Large is more formal than big.

3. Except in large cities, specialist bookshops for children’s literature are few.
4. Countries which are planning to build medium-sized and/or large wind turbines over the next few years include France and Holland.

You can use big, but not large, to suggest that something is important or impressive.

5. Chicago is to him the Big Town.
6. …his influence over the big advertisers.

You normally use great to emphasize the importance of someone or something.

7. …the great English master of classical architecture, Inigo Jones.

However, great can also be used to emphasize size and impressiveness.

8. …the beach of a great curving bay in the west of England.
9. Gardens lay wasted in order that great office blocks and car parks might take their place.

Both big and great can be used to emphasize the intensity of something. Great is preferred in formal writing.

10. You must find this a big change from the Navy, Mr Rutland.
11. Most of them act like big fools.
12. He switched from one task to another with great difficulty.
13. Effective analysis and recognized techniques can bring about a great improvement.

You use large or great to describe amounts. You do not use big.

14. She made a very large amount of money.
15. …drugs taken in large quantities.
16. Young people consume great quantities of chips.