That would be mainly down to the integral "I" term in the PID controller. As Dean says, you could get a good looking response - but with an error if you don't tune it right.

I've got a feeling the cncdrive software actually shows you the response graphically but I may be confusing it with DMM? You want a good response without a noticeable overshoot and no bouncing about afterwards (you want it to be "critically damped").

Tuning a PID is a bit of an art. Here's how I do it:
Start by turning I and D down to zero, then increase P until it's unstable and back off a bit. Then dial in some D until it's unstable and back it off a bit. Then fiddle with both until it feels about as good as you can get. At this point you will have a pretty snappy response - but without the I term, you may end up with a steady state error. So now dial in some I until it's unstable again and back off a bit. You may now need to back off the P and D a little more. Finally, you should check to see what it actually looks like.

Naturally, cncdrive show a slightly different method http://www.cncdrive.com/downloads/help.pdf. It's not a perfect art but you get the general idea.