I tinkered the title of the thread, a bit.  To me larger and big in the same sentence seems a bit awkward, or one choses "larger versus bigger" or "large versus big".

     Now to the bottom line (what matters! he he ).    However it´s difficult to

add something after the superb, to-the-point and clear-cut explanations of Fran or Dale and others here.

     Indeed the following is a bit of a search in the Web, I am with plenty in my plate right now...I agree with the authors anyway, any of you can make further corrections, tough, if any.

     Thanks.

     http://www.perfectyourenglish.com/usage/big.htm

Big and large are used mostly with concrete nouns – the names of things you can see, touch etc.
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.)

http://en.allexperts.com/q/General-Writing-Grammar-680/2008/5/Difference-bewteen-large-big.htm
Answer
large

Of greater than average size, extent, quantity, or amount; big.
Of greater than average scope, breadth, or capacity; comprehensive.
Important; significant: had a large role in the negotiations; a large producer of paper goods.

BIG

Of considerable size, number, quantity, magnitude, or extent; large. See Synonyms at

LARGE

Of great force; strong: a big wind; in a big rage.
Obsolete Of great strength.

Mature or grown-up: big enough to take the bus by herself.
Older or eldest. Used especially of a sibling: My big brother is leaving for college next week.

http://www.english-test.net/forum/ftopic11519.html

As you can see, it can be context-wise.

http://www.schools.nsw.edu.au/media/downloads/schoolsweb/studentsupport/programs/lrngdificulties/writespellsec5.pdf

''...use of general words and colloquial terms, e.g. big instead of large, huge,  giant; sad instead  of   unhappy, despondent, depressed."