If you want to use your Google Voice number for every call, keep the app installed for now
The times, they are a-changin'. Google Voice is slowly but surely being absorbed into Hangouts, and you can do basically everything you used to do in the Google Voice app inside Hangouts now instead. I say "basically" because there's one important function the Google Voice app still offers that Hangouts doesn't — the ability to make calls from your Google Voice number in the native phone dialer.
One of the best features of the Google Voice app today is that it lets you make calls through your phone's dialer, so that every time you make a call it will use the Google Voice number, not the number associated with your carrier. And with the way things work right now in the new Hangouts app, you lose this functionality completely if you uninstall the Google Voice app.
You see, the new Hangouts app (with the help of the additional Hangouts Dialer app) can make free VOIP calls via your Google Voice number. Just open up Hangouts, swipe over and start calling. But the problem is that the hangouts app doesn't identify itself to the system as a "dialer" app to work for every call that you make on your phone.
It's messy to keep another app installed, but Google hasn't fixed this problem yet.
That may not sound that important if you just plan on going into the Hangouts app to make calls, but remember that not every call is initiated from the Hangouts app. If you're in another app — like reading an email or on a restaurant webpage — and tap a phone number to make a phone call, the phone will still try to place that call through the standard dialer app, and that phone call will go out through your carrier number (and use your potentially limited minutes) whether you want it to or not.
In order to make sure that every call you make comes from your Google Voice number, and that you can call via Google Voice in situations without a good data connection, you'll want to keep that Google Voice app around.
So here's my recommendation — leave the Google Voice app installed. Once you've integrated Google Voice with Hangouts the app will no longer sync your messages or voicemails, so there's no need to worry about duplicate notifications. You don't even have to open the Google Voice app or put it on your home screen, just make sure it's set up to take every outgoing call you make from the phone's dialer and route it via your Google Voice number.
This is something Google should be dealing with better, and is something that's pretty easily solved by letting Hangouts declare itself as a "dialer" app for when you go to initiate any phone call, but right now it's our only chance to keep things working the way we knew before.