One thing I really like about Hangouts is that it has a Desktop client/Chrome Extension. Whatever you call it. I can chat on my computer without taking my phone out of my pocket.
A Quick look and it what I could see then there only a phone client. And you can only have it active on one device at the time. So no Tablet and Phone active at the same time. (I know that it runs on phone number. But you could just verify the new login with manual entering a code on the tablet/Desktop. Og even make it optional to link to your Google Account.)