The offset vs output current is likely an effect of heating from the power loss in the OP-amp. For this reason precision amplifier should not drive much current to keep the power consumption constant. It is not only the mean temperature, but already temperature gradients on the chip that can effect of offset.
For the comparison there are different properties that may be relevant for an OP-amp. Sometimes a pA of input current makes a difference and often not. There can be other factors too, like the CM range, linearity (with a low power amplifier the output cross over can be an issue), EMI sensitity, input capacitance, voltage gain (here the ADA4620 looks good with light load, but not so much with more load), drift over time and temperature,....
Some of the points may not even be in the datasheet.
So there is rarely a true 1:1 replacement. What amplifier fits depends on the circuit.