I use OXFROD dictionary to look up for "big" and "large" English definitions, and I use WebCOLL to find which word can put behind them.
big adj.
1. large in size, degree, amount, etc.
e.g. It’s the world’s biggest computer company.
2. (informal) older
e.g. You’re a big girl now.
3. important; serious
e.g. She took the stage for her big moment.
The followings are the words which people put behind of "big" and it's frequence in top 10.
hit
1396
brother
665
band
647
break
573
city
552
name
446
success
401
fan
334
problem
331
screen
317
large adj.
1. big in size or quantity
e.g. A large proportion of old people live alone.
2. wide in range and involving many things
e.g. Some drugs are being used on a much larger scale than previously.
The followings are the words which people put behind of "large" and it's frequence in top 10.
number
12617
amount
4316
part
3514
city
2912
scale
2135
area
1714
group
1622
portion
1373
quantity
1306
population
925
According to the WebCOLL and OXFROD dictionary, I find that there is no obvious difference from "big" and "large". Their common meanings is similar, but which word can put behind of "big" or "large"? In my opinion, I think that people use them in the habit.