My assumption is that only the Samsung email client has the hooks in the app that allow the watch to communicate directly with it (via BT or remote connection). There's no standard (yet) for apps to communicate that level of information to a watch, so there's no way for the watch to get that information from any other email app residing on the phone. The reason you can get notifications from any app (but not full content like a message) is because notifications are a standard of communication (app to phone notification bar) which the watch is able to access.
Someday someone may create an API that allows apps to provide info like full message content directly to a watch, but honestly this would likely come from Google under AW, since there's no incentive for Samsung to develop something like this. They would rather keep their customers buying their watches and phones, so they will always work best with each other.