I've used the Amazon InDesign Kindle export plugin, and I've used Kindlegen via the Kindle Previewer utility, and Kindlegen is far superior. I found the best results by generating an epub, making the necessary edits manually (by extracting, then re-packing the epub) and then opening the epub in Kindle Previewer to make the conversion.
1. Critical problem: the InDesign plugin failed to acknowledge the TOC in my book, created according to the Kindle guidelines. You could export the mobi file to another format using Calibre, in order to edit it, but the easier way is to work with the extracted epub file, and create and edit the guide section of content.opf to indicate the location of the TOC. Then you can easily generate your mobi file again.
2. Footnote numbers and footnote superscripts, when created with the InDesign plugin, had ugly square brackets. Generating the mobi file by converting the epub with Kindlegen produced nice, normal looking superscript footnote numbers.
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