By omitting "/v1.0" from the path it makes the actual URL's far more durable, as they're not version dependent. There are pros and cons to this, as there is with everything. In Azure's case it's great, as you can then use URLs as resource identifiers and put ACL's on them. If they were versioned via the path, this wouldn't work.
Other services, such as XBox, and (very old) Azure, put the API version in a custom header (x-ms-version, for example). This proved to be extremely problematic, and every team that does this had stories of all the problems it caused and then spends time removing it.
I've never seen a detailed proposal for putting API version in the Content-Type header, and will go look.
The content-type header does seem to have many of the same drawbacks as putting the version in a header (any header). For example, people could not make queries from a browser just by entering a URL as there is no way to specify a header. Nor could someone bookmark an API GET request, which is also quite handy.
Ease of use is huge, and I am in the camp that a version in the URL (path or parameter) is much easier in every way than a header. Every with curl, it's easier (I can never remember how to specify headers w/o the man page).