Should I just use the KML Download Link?
The KML Download that is linked to from this website is a direct link to the same KML you can get by going through the My Maps interface. This option will get 100% of the data for the vast majority of maps.
However, the download is limited to 1000 features or 5MB, whichever is less. In addition, certain custom 'typed' data that was set (such as currency) via the Maps Data API may not be included in this KML download.
Is everything transferred to Fusion Tables?
All your map features should be transferred to Fusion Tables if you select to make the transfer for any given map. You can even render the data using the Maps visualization of Fusion Tables, and download a CSV export of the data from Fusion Tables.
Your KML styles will also be exported to Fusion Tables in a 'style' column along with other extended data, but because Fusion Tables does not currently support the same KML styling as My Maps, it will be ignored when rendering, and when exporting a KML from Fusion Tables the Styles will show up as Extended Data rather than inside a standard Style tag.