What is the benefit of using the Servo.
The servo continuously corrects DC offset without any adjustment. If the offset drifts over time and temperature, you won't have to worry about it. You might worry about that if you're using the chassis in situations where the ambient temperature changes dramatically.
What is the down side of using the Servo.
It's more complex and adds a bit to the cost. It's only effective to within the specs of the part used in the servo, so it's possible to get lower offset by manual adjustment, at least for a while. Some people claim it screws up the extreme low end, but that's not borne out by measurement. API didn't do it, if that matters to you.
Keep in mind that, since the output is transformer coupled, there is no DC output in the signal in either case. The only reasons to correct DC offset are to keep the op-amp happy and possibly increase headroom by a few fractions of a dB.