The problem isn't the Apple TV or Netflix. I watched a flawless movie on Netflix on my Apple TV last evening, just as I am sure thousands (millions?) of others did as well. You and a few others have isolated reports here. Doesn't this tell you something about your own system? Again and again this forum and others have reported the conclusion that if Apple TV isn't working well, the problem is your internet supply to it.
The Apple TV didn't kill your router. I don't see how that's even possible. Clearly the router you replaced was deficient. Two possibilities seem likely:
1. Your internet provider is having problems; not an unknown problem.
2. Your own home system isn't working right. If your Apple TV isn't hard-wired to the router, and relies on wireless connection, then you have a poor wireless signal to the ATV, or you are getting interference from a neighbor or some other device in your home. If this is working better with Airplay, then it indicates your iPad is located better than the ATV to receive internet signals from your wireless router. Have you tried directly connecting your router to your ATV via ethernet cable? This would help show whether your problem is with your internet provider or your home wireless system. My bet would be that it will confirm your home wireless connection to the ATV is deficient.
I'm convinced that the reason I don't have the problem you report is that my wireless router (Apple Time Capsule) and ATV are located very near to each other. Try locating them nearby, or direct connect using ethernet (as I mentioned above) and I believe you will find Apple TV as constantly enjoyable and reliable as I do for nearly all of my TV viewing. If you get the wireless connection right you will like it too.