Why does smaller step show instability better?
Here is what I think is going on: 

The stability is increased by a more heavily compensated amplifier. When working in a linear manner it has a gain-bandwidth product of about 1MHz typically. 

In the second case, the change is small so the amplifier behaves more linearly, but in the first case the response is limited by the slew rate of a few hundred mV/us, so it behaves somewhat like it is more heavily compensated, more like tens of kHz gain-bandwidth product. 

This has the danger that it could oscillate in a limit cycle if the compensation is insufficient- the size of the oscillation would be just big enough for the slew rate to limit its growth. From the datasheet.