As mentioned at the title, I would like to ask the if there is any difference or nuance between "当たり" and "につき" in terms of the meaning "every ~". Any case that they cannot be used interchangeably?
For instance, do the following sentences (if they are grammatically correct) convey the exact same meaning?
卵は一人につき二つまで ＝ 卵は一人あたり二つまで
一ヶ月につき一回東京へ行く ＝ 一ヶ月あたり一回東京へ行く