Google Translate is not currently based on neural networks. The best NMT approaches are better than Google Translate, but they're currently too computationally intensive from what I've heard.
I agree Google Translate hasn't improved in a while. It's probably because so much new research is focused on neural nets, not on improving the classic statistical translation approaches.
Facebook, though, I think they DO use NMT. Reasons:
1. They employ many famous neural net people, but not any experts on statistical machine translation that I'm aware of.
2. They came into the machine translation game fairly late. It would be odd to start off implementing an approach perceived to be on the way out.
3. Translation between closely related languages (e.g. Norwegian and Swedish) is far, far better on Facebook than in Google Translate. This is one thing I expect to be a strength of neural machine translation.
They can probably afford to burn more computational cycles, since it's not an on-demand service in the same way.