Here's the rub: HDMI carries stereo or surround sound. It does not carry both.
While some receivers may have dual decoders and DSP controllers to take zone 1 surround sound and convert it down to stereo, most do not. So, when using zone 2 stereo audio, the only way to get it is by running analog audio between the source and the analog (red/white RCA) inputs on the receiver.
By running a HDMI cable between the two receivers, the main zone can use it's DSP to properly handle surround sound.
The secondary output pushes surround sound to your second receiver, which then can use it's internal DSP to run the audio however you would like with ZERO impact to the main zone! This is great because you can run 5 channel stereo, surround sound, mono, or whatever other DSP option that the Pioneer offers you.
HDMI made a huge mistake in not requiring stereo at all times and then offering an option of surround sound for sources which support it. But, that is why I recommend the HDMI cable between the two locations.
As well, the all digital connection of HDMI over that distance should be just fine and well pretty much guarantee the best possible audio quality to the second receiver and your outdoor speakers.