Translation:What did you think about the gift that was given to you?
Both "given you" and "given to you" have been correct English since at least 1800. Google Ngrams shows that with passive "give" the bare objective ("given you") was greatly preferred throughout the 19th century, but was also in steady if slow decline. In the 1960s both forms became equally common in both American and British English. Since then the "given to you" form has been more common, but both forms remain common and both are correct.
But את ניתת means literally "you were given". That's not at all what I mean. In English, "you were given" can mean the same thing as "given to you". It's just a different word order, that's it.
Just like saying.
I gave a book to a boy. A book was given to a boy.
I gave a boy a book. A boy was given a book.
Probably I do not really get what you mean because these verbs really work in a different ways in English and Hebrew and my English is not that good. That's the reason I am talking about it. My comments are applying to the understanding of the hebrew sentence in the first place
I would translate them the same - מתנה ניתנה לך. Because they are both passive in English, the only difference is the word order, and the emphasis, and in both examples the gift is the subject (even though it's actually the object, but because it is passive, it becomes the subject and the verb needs to correspond to it).
Your second example נתנו לך מתנה I would personally translate as "somebody gave you a gift". It's active after all, but it doesn't say who did the giving, so I'd translate it as "somebody".
But in the end, we are discussing English, of which neither of us is a native speaker, so in the end we could both be correct or both be wrong.
I personally care more about correct understanding of how hebrew works and not discussing English :) I can not see how this are the same sentences. You were given a gift - YOU were given. A gift was given to you - GIFT was given. Objects (subjects? I am not that good with grammar terms) are different, aren't they?