All the goodness of the first party camera's deep fusion, etc, is exposed to third-party developers. So if you're using a third party app (that knows what they're doing) then at worst you get the same results as the first party camera.
Here are some things off the top of my head that you don't get with the first party camera, excluding RAW:
Manual focus, Control over ISO vs duration, Manual white balance, Explicit control over which lens is being used (the first party camera switches without telling you), tell what parts are clipping or hitting your noise floor (histogram, waveform, and zebras), focus loupe and focus peaking that tell you exactly what is in focus (rather than tapping and hoping for the best) a reviewer lets you view the component images that make up the image asset in your library (e.g. depth data on portrait photos)…
With MKII, we're now investing in education to help beginning photographers become better.
That said, writing this out are just the checkboxes on a spreadsheet of features. It's harder to quantify the value of design. While we think the first party camera is great, it's also tasked with doing many, many things, from videos to panoramas.
Halide is designed to only shoot photos. Not even video, just photos. We're aiming to be the absolute best tool to do that one thing.
I'm not even talking about professional quality video, just "I want to record 5 seconds of my cat being cute." But I guess the reservations are partly that if you added basic video capability, people would expect it to be amazing in the same sorts of ways that it is for stills?
You also get features like a live histogram and focus peaking that can help when shooting even if you aren't going to edit it afterward.
Can't try the new version yet because of an update bug, but I like the old version a lot.
"Halide’s Depth mode lets you capture Portrait mode shots of pets and people — even if Apple’s Camera app can’t. "
That feels it makes it more similar to my Samsung where I can choose what to "Live focus" on and create fake depth (although I feel Apple's people-only system allows them to recognize and transition borders better)