As soon as you decide to create two URLs such as /user/1.json and /usr/1.html you are creating two distinct resources. The litmus test for determining if two URLs refer to the same resource is you do a GET on both and only one of them returns a 200 the other returns a 303 with the Location header set to the URL that returned a 200.

That's a good reason to differentiate by header (plus no .jpg vs .jpeg shenanigans in the url). Though I can't say I've ever heard of it being used... I'll have to keep it in mind if I'm ever architecting something that anticipates many different kinds of clients in a large API, however.