Client.Platform or Client.Product should get you the details you're looking for but that shouldn't be necessary.
If you create a list of MediaObjects with all the available stream types, the clients are supposed to "intelligently" select the best stream type for their capabilities. The key is to provide as much metadata about the streams as possible. Specifically container and codec types as well as bitrate where applicable.
Client.Product was exactly what I needed. Why isn't it documented? :-)
Because in theory you should never ever have to check for a client's platform or product. Just list all the available versions of a video or stream and let the client/server decide which one is best/most compatible.