Am not sure where we stand today, now that we can forget all about CO2 sensors ...
The two most important rules used to be
"Always know your pO2!" and
"Complacency kills!"
The "rebreather state of mind" starts and ends there, I believe.
Sure ended there for some poor sods not heeding those words.
In between there are other diffrences in the state of mind, depending on whom you trained with and to what level.
The venerable
"If in doubt, bail out" (usually referring to OC bailout) for example is something often considered
an OC state of mind, versus
"stay on the loop as long as possible".
But for most part, the different state of mind really centers around dilligence, disciplin, awareness, attention.
To your gear, to yourself, to your buddy if you've got one. Before, during and after the dive.