Host your data on your own site
Why? Because your data belongs to you. Not to third parties with their rules, subject to change, whenever and however they see fit.
That being said, this does not mean your data needs to remain only at your place. You can syndicate the data to those third party sites.
Migration of data
In my case, hosting my own data is currently a work in progress. Which is why certain parts of my content can only be found on Twitter and CodePen, but will soon be here as well, once the migration has taken place.
To learn more about the #indieweb movement, head over to indiewebcamp.com.