It's not that simple. The Hebrew of 34:1 has God promising to write on the second tablets the same things that were on the first tablets. Moses is only required to prepare the stone so it can be engraved. Then in 34:27 when Moses is commanded to write 'these things,' the reference seems to be to what God has just told him, and not specifically to the Ten Commandments. 34:28 does not supply a subject for the writing of the ten commandments, so the verse by itself could be taken either way. The easiest way to understand 34:27-28 in its immediate context would be to say that Moses wrote both the ten commandments and the other instructions. But, unless we assume two replacement copies of the ten commandments, that is inconsistent with 34:1. Therefore although I guess there are multiple possible ways to understand the text, the two interpretations which leap to mind are (1) God wrote the second tablets and Moses wrote other instructions on something else. (2) There are two versions of this story here which differ as to who wrote the second tablets.