Heck, the compass in my smart phone goes wacky sometimes. A functional compass is nice to have as part of a GPS unit because it takes over when the person is stationary (not moving). My GPS unit's compass is much better. Also, a true GPS will be able track multiple satellites, in a noisy environment, or lots of cloud cover or tree cover.
I'd never use a smartphone for navigation while hiking. I would have a smart phone or flip phone with me (in a baggie to keep it dry). You can call in your coordinates read from a GPS unit in a pinch. There are stories of people being lost or injured and calling the local police dept from their cell phone. I was hiking at the top of a 14teener once and called my wife from the top.
To survey a plot professionally, you'd still use the system that you mentioned and unfortunately probably a transit system.
We're mapping in a bunch of huge concrete foundations and dozens of dispersed footings and mounting brackets.
The plant stretched 176 feet down a hillside -- in multiple stages -- with a total drop of over 70 feet.
Most US archaeology is done in arbitrary 2-D layers; this thing is full 3-D -- and we haven't found photos, or drawings -- or anyone alive who remembers what it looked like when in operation. So, we have to have good 3-D measurements for every concrete structure and equipment mounting stud -- and work from there...