If nothing in the system changes aside the replacement of the problem device, it's either the device, or how it interacted with the network/laptop. Not the network itself, network settings, or the laptop. At best it's a failure of the automatic handshaking between the incoming data from the Macbook and the apple TV or some interference between them, which since the Apple TV is the only device having an issue, again it falls to the Apple TV as the problem.
Nothing else changed, same network, same # of devices, same laptop, same router, same locations, same internet connection speed. All that changed was swapping out an older Apple TV for the new generation. If it was a network bandwidth issue, or laptop network setting that was creating the problem, changing the device that the laptop was streaming to would NOT fix the issue, it would still not be able to stream fast enough to work smoothly to any device. I'd see the same problem streaming to the TV directly, or to a Fire Stick, etc. and I don't. It also would mean that no device would stream at a similar quality level to the Apple TV.
I'm not saying that in the original poster's case that trying different network settings etc. might not fix his particular problem, but once all of those options are exhausted you start to look at hardware. It's well documented many people have had problems specifically streaming from a Macbook's to Apple TV's, when the ONLY problem is the Apple TV itself, streaming from the macbook to other devices worked fine, and so did streaming from other sources (iphone etc.) to the Apple TV.
At the end of the day I don't really care what the underlying technical cause is. If I have 20 devices on my network, none of which have problems with bandwidth, streaming, etc. and the Apple TV is the only problem child, and replacing it fixes the problems, that's all I need to know.