Heyyo! I'd first just like to thank everyone who's shared their own thoughts and opinions so far! You all rock.
I like to think of it as finding a healthy balance (like a good, nutritious diet?); giving equal attention to both the image and sound on set - treating them with equal "value" as storytelling elements. Shot by shot, scene by scene, consider the impact both can have on your story, and what each needs to achieve - compromise smartly. While a "perfect scenario" where every department gets everything they want is exceedingly rare, it's key to focus on what's going to be important for the story.
On one hand, there's definitely some moments where sound can indeed take a backseat - for example, fight scenes are almost entirely created in post. Reference audio is still very useful for syncing sound effects later, but that's an instance where it may be the smart choice to use an onboard mic, if your location is really limited for space. (Never hurts to boom if possible though - a lot of the sound in some of our shorts like Fan Friction and London Brawling actually use a lot of production sound in addition to post-added sound effects). In our experiment short, the ninja scene with the pillow and karate chop play pretty similar between both versions, because the emphasis is on sound effects.
On the flip-side, there's times when sound should absolutely be a high priority, if not the top priority - particularly if an actor is doing a very emotional or intense scene. These scenes can be the most painful when sound isn't provided the opportunity to record the scene optimally. If you end up with poor audio, the two options are either use what audio you have from set, cleaned up as best as possible (hoping it doesn't distract the audience too much), or, try to get the actor back to recreate the performance in ADR - while ADR may be easy for some actors on simpler dialogue, it's extremely difficult to recreate a dramatic, intense performance, while hitting lip sync. While I won't call them out directly right now, there's a couple moments throughout VGHS that would have benefited from giving sound more priority - we ultimately overall tended to go with using production sound, even if it was a little (or extremely) rough.
What I found really interesting when we got to editing the two shorts was how different the audio really ended up being based entirely on where each team had their respective microphones - it was the time, consideration, and effort that made the difference.
I'd like to stress how a lot of the quality of your film comes from how you use your equipment, not what the equipment is.
Even if you're using your phone to record sound, take a moment to test it out, and try to place it somewhere that will pick up the actors' performances cleanly. A well-placed cheap recorder can still outperform top-of-the-line gear if it's used better!
As a random aside, I actually liked the look of the iPhone for the theme of our short - I thought it added a nice pseudo '80s look I find that people acclimate to image quality pretty quickly (we can still watch older films usually without complaining, or an old DVD without being bothered by the lower resolution the entire time), and while this is also true for sound (we can still watch something in stereo even if there's a surround sound version available), production sound is primarily about capturing something cleanly and intelligibly - and if you can't understand it clearly, that's something you can't ever expect your audience to adjust to!