They both end up at the same place:
The trouble with the 'Ask' option is that it encourages putting the entire question in the title;
The 'New' option is far clearer that the 'Title' is separate from the 'Description'
The 'New' button appears wherever a forum exists. To remove it would mean customising the banner where it exists (I am planning to look into how much effort this would be).
We added the Ask search bar to try and get people to search exiting questions before asking their own. The Ask button doesn't do anything unless you've entered something first. This is my preferred journey for a user.
I do agree, having one or the other would be a cleaner experience so I've added it to my forum revamp project.