I always use large, larger, & largest instead of big, bigger, & biggest. Large/larger/largest seem (to me) to sound better and seem to have a better feel when written. From a purely semantic point of view, are the above true synonyms? Are there contexts in which one is to be preferred over the other? Synomyns like quick, fast, & rapid do not seem to be true synomyns. certain contexts seem to prefer one over the others. BTW: I think English has far more words relating to speed than most languages.
I use large in formal settings, but if I'm dealing with kids I think Big has a greater impact if I'm describing the size of something.
IIRC they generally mean the same but sometimes there can be some slight contextual differences. In other languages largest means widest and biggest just means greatest in size(or possibly volume), large being the french for wide. So traditionally there was a slight difference but now we tend to interchange the words.
"Big" is the more general word and is used for dimensions other than size. E.g., importance (a big problem), notoriety (a big idiot), maturity (you're a big boy now), age (my big sister), influence (don't mess with big oil), popularity (soccer is big now), or generosity (he's a big enough man to forgive his enemies). "Large" is generally limited to size, although colloquially it is sometimes used as a synonym for "big," such as "an unimportant man given to large gestures." The basic meaning of "great" is size, and it usually means bigger than "big," such as "the president wields great power," or "a great fire destroyed half the city." But it is also a common superlative of "good," e.g., "I had a great time," "she and I are great friends," "the inauguration was a great occasion," "Robin Williams is a great actor." We could have the same discussion contrasting "small" with "little."
Fraggle Rocker: Bingo !!! You are correct. I did not think of those uses of Big. Large would not be used.