- 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