It depends what you want to share though. Are you sharing the location of a resource or are you sharing a specific version of that resource?
If I'm viewing some resource in some client that supports version X and I send it to you and you view it in a client that supports version Y (maybe this happens automatically, maybe new versions are in the process of being rolled out, maybe your on the mobile client that hasn't been updated yet) isn't it better that my client gets a representation of it that it can understand?
(I don't think there's one answer for everything, I think both can make sense in different situations. But I think versioning via Headers can be very powerful and can interact well with of RESTful types of things you might want to do, it would certainly make no sense in an RPC style API)
If I'm viewing some resource in some client that supports version X and I send it to you and you view it in a client that supports version Y (maybe this happens automatically, maybe new versions are in the process of being rolled out, maybe your on the mobile client that hasn't been updated yet) isn't it better that my client gets a representation of it that it can understand?
(I don't think there's one answer for everything, I think both can make sense in different situations. But I think versioning via Headers can be very powerful and can interact well with of RESTful types of things you might want to do, it would certainly make no sense in an RPC style API)