How to hook-up old apple TV to Sony Bravia 55" TV and Audio amp without HDML

if the tv does not have hdmi then few things would work because of hdcp High-bandwidth Digital Content Protection - Wikipedia

if what you mean is you wish to connect the appletv to both a tv with hdmi and a amp without hdmi then you can get a splitter

Amazon.com: iArkPower HDMI Audio Extractor Splitter HDMI to HDMI + Optical + RCA L/R Stereo Audio Out Supports 3D (1080P): Electronics

Is one method better or easier than the other?

If you can use TV passthrough, then the TV acts as an Audio Extractor, and then you won’t have to buy an external Audio Extractor. I feel that is easier for most users. The audio quality is not affected by the which method you choose, as you audio system sets the bar for that.

Using TV passthrough also means that you can use your audio system for any TV use, including any connected device, with superior audio (compared to TV built-in speakers). Using an external Audio Extractor would have functionality only for one device (Apple TV in this case).

You may set the TV to passthrough the audio over optical or RCA to an audio system.

Then also change the Apple TV Audio Format to Dolby Digital or Stereo.

Apple TV →[HDMI]→ TV →[optical]→ audio system

It's easiest (and cheapest) to connect the ATV using an HDMI lead to the TV. The TV probably has an optical (TOSlink) output and if your Amplifier has an optical input you can connect to that with a suitable lead. This shohld passthrough Dolby Digital 5.1 (though no 7.1 or Atmos).

If the amp has only RCA (phono) jack inputs then you will need a lead from the TV's 3.5mm headphone jack to RCA jack connectors to go into the amp. This will passthrough only 2-channel, so stereo or Dolby Stereo (which is stereo with the rear and centre channels matrixed in, and requires the amp to be able to decode it and to provide centre and rear speaker outputs). Dolby Stereo can be listened to as plain 2-channel stereo perfectly well.

You’ll have to ask NAD about that for a definitive answer, but I don’t expect ill effects. No moving parts that can wear down, and power spikes is what hurts electronics most.