When converting from EPUB to a Kindle format, you want to convert to AW3, as it preserves the formatting -- MOBI only supports a subset of functionality, and doesn't properly support styles.
Once you already have a MOBI (Amazon typically names these *.azw) there is nothing to be gained from converting it to AZW3, unless as HarryT says you want to edit it.
You could of course convert it to EPUB, edit it there, and reconvert for your Kindle, but the editor does directly support AZW3 too.
Personally I prefer editing EPUB -- opening and saving an AZW3 takes longer.
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