A big part of the Android Wear 2.0 update is the inclusion of Google Assistant. If you've never used it, Google Assistant is like a friendlier version of Google Now that can remember things and help you by doing more "stuff" than the original could. It's pretty cool, and even though it's not been around for long we've already seen it get better and smarter. And now, it's on your watch.
Assistant is on different devices with different hardware and different abilities.
That means you can tell your watch to do things like add milk to your shopping list, tell you the weather or how traffic looks for your evening commute, or even play a movie on your Chromecast. It can do all those things and will. But Google Assistant acts differently depending on what device it's running on, and there are some things your watch can't do as well as other devices can and even some things your watch can't do at all. And you'll notice that right away if you already have a Google Home.
Google Home can't show you pictures of cats if you ask it to. If you have an Android TV, it will try to show you pictures of cats on it but will eventually tell you that it just can't do that. It makes sense because Google Home has no display. Your watch can show you pictures of cats but it also has limitations, and it's not going to be able to play the latest episode of your favorite Netflix show. It's a little frustrating but expected. At least until LG or Motorola makes a version with a projector module, anyway.
If you have both a Google Home and a new Wear 2.0 watch, things can get even more frustrating. Google Assistant doesn't yet "decide" which device is best to use when trying to answer your questions. By default, any time Google Home can hear you ask Assistant to do something, it will try to do it. Even when it can't do it, or when you want it to be done through your watch.
For example, if I'm in the bathroom combing my hair and getting ready for work I might want to know if traffic on my commute looks good. If I ask Assistant, and if Google Home hears, it will answer through the Home speaker instead of showing the traffic card on my watch. Or it will do both. Or it won't do either. And there is no setting of any type to tell it what you wanted to be done in a case like this.
Google Home trumps everything else when it comes to the Assistant chain of command.
This isn't something new with your watch and people with both a Google Home and a Pixel have seen the same issues since Assistant became a thing. Your phone will tell you that things are being answered on another device and Google Home will tell you it can do that thing when it can't do it. Google knows what's up here and they have some sort of solution in the works. But that doesn't help us in the here and now.
We don't have any real advice how to get one Assistant to do some things and the other Assistant to do other things. Nobody does, and all you can do is turn off the microphone on one or the other (or both when Google doesn't need to hear things) which isn't very great. But know that it's not just you or something you're doing wrong, and we're all waiting to see what Google does to fix it since Assistant is going to be on plenty of other things in the near future.