There are differences: in the USA the statement is assumed true, and must be proved false if libel is to succeed. In the UK the statement is presumed to be false, and the libel will succeed unless proved true.
I wonder what the GDPR has to say about publishing a private email?
The difference on the UK really comes down to the cost of defending oneself. Engaging in a court case is not a costly undertaking and this would likely be a quick in-and-out case, as long as you have the evidence to backup their claims.
I imagine either party in an email conversation have the right to publish the email, unless some terms were agreed in advance or the subject is expressly personal.
AFAIK, for ordinary snail mail ownership goes to the recipient in most (all?) European countries: You can't claim copyright on a letter you sent to someone else. Can't see why the same shouldn't go for e-mail. If you wanted something to remain “private”, don't give it to someone. (At least not without having them sign an NDA first).