The 340 has the "Cool" factor and came with better parts in stock form.
On a custom build...... I feel (and this is just my opinion) that it really again comes down to ... Do you want to be able to tell people you have a 360 or a 340.
Just build a 360 and tell anyone who wants to know that it's 340....if it matters to you at all (and it really shouldn't matter one iota, if you dont have an original numbers matching 340 car - which you don't).