Exporting from Explore.garmin.com to a GPX or KML creates very large files, and won't import to Basecamp. Is there an in-between I need to use?
The site exports the data specified by the current map filters. If you want smaller files with less data, you might try setting the filters to restrict the types of data included and/or the date range.
I believe that user visibility matters as well. But this isn't usually helpful unless you have an enterprise account. I don't know whether or not collection visibility matters. That might be another thing to try.