Second rounds of nested PCR are typically done to sort out false positives. Visualization of the designed nested shift is more convincing evidence of true product(s) than just the presence of an amplicon(s) alone. If the difference of size is a concern, a higher concentration gel would be of use to discern the subtle differences between your amplicons.

It has more to do with increasing specificity of the amplified fragment than size selection. I do nested PCR when I am doing 3'RACE because one of my primers (oligo-dT) binds all mRNAs and the second round ensures that the amplicon is specific to the gene I am interested in.