If the product and price are the same, I would always buy from Amazon (or a company fulfilled by Amazon), as they have amazing customer service, and a no question asked return policy. You can return headphones you don't like, less shipping. If there is some kind of damage, Amazon will pay for shipping. I returned a Fiio E7, as I didn't notice any sonic improvement with this amp; so I told Amazon that it didn't work properly, and they gave me a return shipping label for free. Also, Amazon (and fulfilled by Amazon) offers free shipping on products over $25 (and usually qualify for Prime if you have it).
--> However, I would only buy from Amazon if they were listed as an authorized dealer for the headphone. Likewise, I would only buy from a company fulfilled by Amazon if that company was an authorized dealer. This is for warranty purposes.
Lastly, some products are heavily faked, and I've read (but not experienced) about authorized dealers accidentally shipping these fakes. If that were the case, I'd buy direct form the supplier.
I've never bought from Head Direct, so I can't comment on any benefits, if at all.