Big vs. Large vs. Great

• They have a big/large house in the city.

Great is used mostly with abstract nouns – things you cannot see, touch etc.

• It was a great mistake.
• I have great respect for her ideas.

Big can be used with countable abstract nouns in an informal style. Large is not used with abstract nouns.

• You are making a big mistake. (NOT —a large mistake.)

With uncountable concrete nouns, none of these words can be used.

• You have got a lot of luggage. (NOT — big/large/great luggage.)

Reference: Practical English Usage by Michael Swan Published By Oxford University Press