Dictionaries will give "Happy" for both.
A Mandarin song has the title 你开心所以我快乐
Question therefore is whether there is any signifying difference in usage?
That is, which word / phrase fits better in a certain context or situation.
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In your case, both 开心 and 快乐 are used as adjectives, which denote “happy”. Translated, the sentence means “I am happy when you are happy.”
However, only 快乐 can also be used as a noun.
This would mean “he obtains happiness from doing good deeds”. It would sound weird if you substituted 快乐 with 开心, which would then make it “he obtains happy from doing good deeds.”