Formal or lingua franca?

A question very common in these times of English language predomination. Nowadays, it is very important to learn English as a second language, but is it better to dominate the formal English than the English used by native speakers? Both have some advantages and disadvantages that I'm going to analize next.
If we learn the English in the "correct" way (formal), then we will speak the English as a book. This can be useful in work or professional embiroments where we need to express formally. However there are a lot of words used by the Englishv native societies as modisms that, in case of dominating just formal English, we could be unable to understand them at all.
Speaking English as a lingua franca could be usefull to feel identified with the everyday English speaker societies.
I can conclude that learning English in its formal state is the best choise, nevertheless, we need to be able to speak as a native English speaker does.