The import / export tool in the admin should work fine between v10 and v11 if you're just exporting and importing core content such as page, blocks and media. Anything custom will likely need something different but you could always using a combination of the Content Delivery and Content Management APIs to load and regenerate content perhaps.
I find the import/export feature to be very clunky in my experience. I would say scripting it viat the API's would be the way to go. You will have far more control that way. Good luck!
We have fallen into significant technical debt due to lack of consistent upgrades and are currently on version 10 and looking to get to version 11 but due to the amount of legacy code and outdated .NET framework (4.5.2), it will be a very iterative and intensive process.
Another option we were looking at was to install a new v11 and export the live site content from the old site and then import to the new site. We were wondering if there any solutions available to help mitigate this process and make it less manual?