Hangouts does everything you describe. It's what I use all the time. It is seamless across my phone and table and my PC. And it is seamless across windows, linux and apple.
It is seamless between SMS and the internal delivery system, and the conversations are synced to my gmail account allowing me to search them.
I like Hangouts and use it constantly, both personally and for work (I work for Google, where it is arguably the primary means of communication), but it isn't quite as seamless as iMessage in one respect: SMS integration. In iMessage there is no distinction between SMS and iMessage messages; they're all just messages. If they can be delivered via Apple's infrastructure, they are, if not they're routed via SMS. With Hangouts, SMS and Hangouts chat messages are distinct. They look similar, but they're different in subtle ways.
Of course, Hangouts clearly is superior to iMessage if you or your friends use non-Apple devices, because Hangouts works on a much wider variety of platforms, and for those who understand the distinction it's *good* to know what is SMS and what is not, because SMS is inherently unreliable -- and in some parts of the world SMS is also ridiculously expensive while data is cheap.
So, although depending on your context Hangouts may be better than iMessage, it's definitely not as seamless in a pure-Apple world as iMessage is.