'large' is bigger than 'big'
It is huge .
a large vessel or aircraft
a big house
a large room ( or a big one)
'big' also means not only 'big' in size ,it could refer to age as well:
'Your are big boy now.'
You can't say 'you are a large boy' .
'large' could be used abstractly as well as in 'large effect' ,you could use both 'big' and 'large' here ,it is just that 'large' has relatively a greater size than 'big'.