Gene 2 bearing AAAGAA sequence in the middle will produce more full-length protein (length is with respect to more number of amino acids incorporated). This is because no ribosome binding site is present in the middle of the gene which allows the complete translation of the gene by a single ribosome. However, in gene 1, AAGGAG has been encoded in the middle. This leads to a new ribosome binding site (RBS) and calls for the recruitment of a new ribosome at this site. So, the codons upstream of this RBS will be synthesized by one ribosome whereas the codons downstream of this RBS will be synthesized by the new ribosome recruited to the RBS. This leads to the formation of two chains of amino acids, making the length smaller when compared with the case of gene 2.
AAGGAG and AAAGAA both code for Lys-Glu. AAGGAG is also a ribosomal binding site whereas AAAGAA...