I want to clarify something....
I think you're misusing the term, "fresh install".
A fresh install is what you get when you first install XenForo. There are no post, no threads, no users, no add-ons, and no styles. That is what it means by "fresh install" (or clean install).
And so there would be no reason to export and import a fresh install. It would be a lot easier to just install a new copy.
Does this make sense?
Now, what I understand is you are trying to relocate your site.
You have post, threads, members, and I would assume maybe add-ons and maybe styles to go with it. That would not be a fresh install, that would a move.
That is when you move (copy) your files and export and import your database else where.
I'm not trying to pick on you, but rather inform you, because these things seem to confuse newbies. And they end up reading post like this and quoting someone and telling someone else they want a fresh install, thinking it means one thing, when it really means another.
So what you want is to move your site. You're not looking for a fresh install, unless you want both... ie.... To import your current site onto your new host and start up another site (or test site).