The digital readout will fluctuate a lot, but it will maintain an actual mash temperature +/- < 3 degrees without recirculating and +/- ~1 degree with recirculating. I use a dial thermometer with a 12" stem inserted through the lid to monitor and a floating thermometer in the grain bed that I check when opening to stir.
As an example, I brewed a Pale Ale yesterday and mashed at 150 degrees with recirculation. My strike temperature was 159 degrees. After dough in the display read 159 for several minutes and then gradually dropped to 149, at which time the element was switched on. I use 500 watts to maintain mash temperature. The element remained on for about 4 minutes, until the display read 154 degrees. I had the temperature set to 152. The actual temperature remained between 149 1/2 and 151.
I recommend using the false bottom if you're not recirculating. It seems to dampen temperature fluctuations and help maintain mash temperature. You don't need it if you recirculate. Also, if you don't recirculate I recommend a brew bag inside the malt pipe and a BIAB crush. With recirculation, I crush with a mill setting of .042 and use just the grain pipe bottom insert.
The controller is programmed to use degrees Celsius. When using Fahrenheit settings it will use only the closest degree F to the corresponding degree C. This results in skipping F degree readings. In the mash range I used yesterday, the readouts during the mash were 149, 150, 152 and 154. The available settings would be the same. I use the 35L.110V system, but am pretty sure they all use the same controller.
The difference between the BrewZilla and the DIgiboil are the BrewZilla has a built in pump and a programmable controller. The Digiboil has neither, but you can still step mash by manually changing the temperature setting on the fly.