I think there are too many possible variables to say either is always better. But for social inter-connections and/or Single Sign On (SSO) kinds of things, I would suspect ‘me@mysite.com’ would be the least-adaptable.
I used to use one e-mail address for everything (back in my old forums days).
Since I have my own domain, I do the following:
facebook@mydomain.com
twitter@mydomain.com
instagram@mydomain.com
wordpress@mydomain.com
and so forth
so if a site is something.com, I will do something@mydomain.com
That way I will know who sold my e-mail address to spammers.
This is more for the smaller sites. Not accusing Facebook, Twitter, Instagram or/and WordPress of selling my e-mail addresses.
That one e-mail address started to receive so much spam that when I changed it, I had to go through all the other websites and change e-mail on those website profiles.
You know when you change e-mail address, you have to wait for that e-mail where you click a verification link?
So if let’s say WordPress was to sell my e-mail address on my profile…All I do is change wordpress@mydomain.com and not have to change my twitter/instagram/facebook/etc…profiles.
I still have info@mydomain.com contact@mydomain.com contactme@mydomain.com for people to well…contact me.