Just came around this old thread while looking some info about the HP6060B.
In the user manual of the 6060B it states that it can be setup to discharge a battery but it will only stop doing it once the battery voltage has reached ZERO volts, which is probably not a good thing for any chemistry. Depending on what size batteries you intend to measure for capacity, there are better options in the form of smaller electronic loads that I have purchased in the past on the e-place and that allow you to set a cut-off voltage and will read out accumulated battery capacity in both Ah and Wh as the test progresses, along with the voltage of the battery. The ones I have are made in china and so far seem to work well in that sense, and are rated at 60W max, 30V and up to 10Amps. They cost each around $25 US, and they are a bare board with a build-in heatsink and fan, plus two LED displays and a rotary encoder/push button. I've used two or more of these loads in parallel when more than 60W was needed to be handled. I also do have a 6060B which I use to test power supplies.
Hope that is helpful information.