Is it better to use AirPlay to push from Mac to AppleTV, or use AppleTV to pull from a Mac? If we have an iMac and an AppleTV, is it better to use the AppleTV to pull content from the Mac to play it, or is it better to start from the Mac and use AirPlay to push to the AppleTV?
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.