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you asked in English, i think i should write my opinion in English.
i think "very" is a casual word, "quite" is more formal word.
i've never heard the word of "quite" when i talked with my friends using English.
maybe difference of these words is difference of "めっちゃ" and "大変" in Japanese.
Thank you very much.!
Quite can also add stress or importance to the word where as very is only telling us that something is more than usual.
She is very late.
This tells us that she is more than an acceptable amount of late but the emotion is that she is late.
She is quite late.
This gives us the emotion that she is in a lot of trouble because she is late.
We almost never say quite nice or quite worried
We do stress
Quite late
Quite angry
Quite rude
If there is some importance to stress we can use quite instead of very but in daily conversation very is usually enough.