Is it better to use AirPlay to push from Mac to AppleTV, or use AppleTV to pull from a Mac?
Solution 1:
There's no difference in quality, so it's purely a personal choice and depends on how your home network and systems are set-up.
I have a Windows PC running iTunes 24/7 and that has my entire library of music and video on it, so the Apple TV can pull whatever I want from it.
Sometimes I'll play content such as BBC iPlayer or Youtube videos from my phone, or from my laptop if I've downloaded a video I want to watch without importing it on the other system but it really makes no difference. It's just about convenience really.
The only thing that really makes a difference is network connection for the caching, wired ethernet is obviously a lot faster than WiFi.
Solution 2:
For many things, it doesn't matter but AirPlay only does 2 audio handles while the ATV can do multi-channel audio so it can play a 5.1 soundtrack when streaming iTunes. I encode my TV shows with both stereo and 5.1 soundtracks and the audio difference is obvious when I use AirPlay.
Solution 3:
In my system, pushing from Mac works more reliably. Pulling from ATV sometimes gets drop-outs, but pushing from Mac is nearly flawless. For this setup (push from Mac):
Downside: you can't listen to iTunes on your Mac and push different iTunes content to the ATV.
Upside: you can blast the music to your Mac speakers and the ATV at the same time, and walk around your house and hear the same music in different rooms (if they are in different rooms).