Thansk, i believe the simulation is fairly accurate, so i dont think they're acting like comparators(?), and surely theres not a "problem " with outputs "trying" to go below ground(?).
Our worry is that the single supply opmap may suffer slow bandwidth when its output is near zero volts, and therefore, its output voltage woudl be more distorted and delayed compared to the split supply opamp.
Indeed, i believe opamps behave best when their inputs and outputs are inbetween the supplies, or at least 1.2v away from them....even though LT1013 is rated as being "rail to rail input and output", i still suspect the single supply version will be distorted in comparison with the split supply version? (not in the sim but on the bench)