Well thanks to antitrust concerns they are pretty much independent and it still has the same awful UI and bugs of the app before it was sold. Really wish it could benefit from Google Maps (especially for POI search!).
Waze could certainly benefit from some wise UX choices the Google Maps team long implemented. Namely the ability to choose any start location and swap it with the end location to get round trip time estimates.
It does give you some options, but then it starts to feel like you're doing the work instead of Waze (why can't they diff the results and just show you the POIs?). The predictive search is just awful, you'll see results from all over the country (and sometimes world!) when you're looking for something a few miles away. There are frequently duplicates in the list and adding to the issue is that the list view also contains so little information that it's hard to see if the result is the one you're looking for. Google Maps absolutely blows away Waze in terms of search UI.
Other gripes:
It suggests using HOV lanes despite not knowing if there is someone else in the car, that can dramatically effect routes (say route A is faster only if you can use the HOV lane).
For ferries (I live in Seattle) it doesn't count the time on the ferry which can give you wildly incorrect time estimates. There's also not a way to ask for a route that doesn't include a ferry (sometimes you can drive around). For example Google Maps suggests 1:04 to get to a spot on Bainbrdige for me right now where Waze says 25 minutes. Considering the ferry ride itself takes ~30 minutes...
I agree they need to revamp their HOV situation. In my case, I have a car with an HOV sticker and I don't know if it's measuring HOV lane traffic separately from non-HOV traffic (huge difference in the Bay Area on the 101)
@jonknee is your name jon kneeland? I'm a John Kneeland. Small world!
I find Google navigation UI more confusing because it puts alternative routes on the map whilst I'm trying to find the route and drive at the same time. I just want a clear bold line showing me where to go. Waze gives me that and only gives out more info when stationary where my brain can handle it.
There hasn't been any news on this for a while, but Waze has also stayed almost exactly the same. There's a little integration the other way (Google Maps sometimes shows incidents reported on Waze), but that's it.