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 still a work in progress. I started with my blog posts and a bunch of other things. In September 2017 my code snippets — until then only to be found on CodePen — finally came home. Now it is only a matter of time until the stuff I tweeted before 2016 joins in.
To learn more about the #indieweb movement, head over to indiewebcamp.com.