bigとlargeは言い換え可能な場合とそうでない場合があります。いわゆる「大きい（大きさ／広さ）」については、言い換え可能です。ですが、big には他の意味もあって、たとえば、big brother (兄) では「年長の＝older」という意味です。
英単語の正確な意味の範囲を知りたいときは和英辞書ではなく英英辞典（OxfordまたはWebster）をご覧になることをおすすめします。
largeとbigについては、少し文字化けしてしまうかもしれませんが、以下にOxford Dictionaryの説明を貼付けますので、ご参照ください。"big"のさまざまな意味の１つとして"large"があることがわかると思います。
large /l??d?; AmE l??rd?/ adj. (larger, larg●est)
1 big in size or quantity: a large area / family / house / car / appetite ?a large number of people ?very large sums of money ?He's a very large child for his age. ?A large proportion of old people live alone. ?Women usually do the larger share of the housework. ?Brazil is the world's largest producer of coffee. ?Who's the rather large (= fat) lady in the hat?
2 (abbr. L) used to describe one size in a range of sizes of clothes, food, products used in the house, etc: small, medium, large ?It's better value if you buy a large box.
3 wide in range and involving many things: a large and complex issue ?Some drugs are being used on a much larger scale than previously. ?If we look at the larger picture of the situation, the differences seem slight. ?note at big
big /b?g/ adj., adv.
?adj. (big●ger, big●gest)
LARGE|
1 large in size, degree, amount, etc: a big man / house / increase ?This shirt isn't big enough. ?It's the world's biggest computer company. ?(informal) He had this great big grin on his face. ?They were earning big money. ?The news came as a big blow.
OLDER|
2 (informal) older: You're a big girl now. ?my big brother
IMPORTANT|
3 [only before noun] important; serious: a big decision ?Tonight is the biggest match of his career. ?You are making a big mistake. ?She took the stage for her big moment. ?(informal) Do you really think we can take on the big boys (= compete with the most powerful people)?
AMBITIOUS|
4 (informal) (of a plan) needing a lot of effort, money or time to succeed: They're full of big ideas.
POPULAR|
5 ～ (in ... ) (informal) popular with the public; successful: Orange is the big colour this year. ?The band's very big in Japan.
ENTHUSIASTIC|
6 (informal) enthusiastic about sb/sth: I'm a big fan of hers.
DOING STH A LOT|
7 doing sth often or to a large degree: a big eater / drinker / spender
GENEROUS|
8 ～ of sb (usually ironic) kind or generous: He gave me an extra five pounds for two hours' work. I thought ‘That's big of you’.
