If you look at the topology of the Adafruit design, the power to run 5v loads has to come from first being regulated down to a plausible battery voltage, and then boosted back up. That particular board is made with components that try to support a lot of current through that path, and warns that the upstream supply needs to be quite capable to match what the board can do.

But that kind of regulate and re-boots topology, if done with lower rated components, could easily explain the kind of issues seen here, in that it can impose a bottleneck on how much power can get from the USB input jack to the USB output one. We still don't know what is on the powerdock and how it is configured, but it's not hard to imagine limitations there.