In an informal style, big is more common than large.
- – He has got big / large feet.
- – They have a large / big house in the city.
We use great with abstract nouns – the names of things which we cannot see or touch.
In an informal style big is also used with countable abstract nouns. Large is not used with abstract nouns.
- – I think it was a big mistake. (BUT NOT I think it was a large mistake.) None of these three words are used with uncountable nouns.
- – I have got a lot of luggage. (NOT I have got big/large/great luggage.)