'Honoured' Is suitable for a formal occasion: accepting an honorary doctorate, for example, or for something very serious. 'Flattered' is an honest description of how you feel, and is the usual way of expressing it in everyday speech.

"Thank you, I'm honored" is appropriate for a very festive event. "Thank you, I'm quite flattered" is a more common example.

Thank you, Diego. What kind of invitation? To the my new friend's country, for example.

What kind of invitation is it? Unless it is to some major event that is selective about who can attend, I think both are a bit much to say. A customized Thank you would be more natural. Something simple like Thank you for the invitation or Thank you very much.