Systematic error must be very low, as it is your first simulation , but the second simulation gives you very big input referred offset voltage. Therefore , this means that when you put your amplifier in unity gain feedback, something goes wrong. What type of amplifer you have? Telescopic or folded cascode. You should be careful about input common mode range voltage and output common mode voltages. They should be compatible. You may put one of the input transistors into triode. Please check you amplifer dc points.