I would give up my US nationality for more freedom without a second thought. The US currently invades privacy and personal choice way too much, both in this country and abroad, and creates many freedom-infringing laws to imprison more people than communist Russia or China for victimless "crimes." I would give up my US nationality for nothing because this country is an embarrassment to me. If I could leave and go back to Europe where my family came from I would.
Maybe not for marginally more freedom. I'm not moving to Amsterdam just to get the freedom to smoke pot (though as its similarly free it's not like I couldn't be persuaded to move there if I visited and found it enchanting enough). But if it was a substantial difference I would leave America.
I would hold onto my nationality, because it means that I
1. Can legally live, work, study, and own property here
2. Am protected by police and firefighters
3. Can vote
4. Have citizenship here.
6. I can run for public office
That covers pretty much everything apart from civil rights and whatnot.