Definitely phones charge faster on a plug in wall charger ( as well as most plug in car chargers ). I suppose it's better if the ( external ) battery has a larger maximum current output so the device can operate power sucking apps and charge the internal battery at the same time. Most Li-ion batteries are not recommended to charge at a rate over 1000ma. Not to worry though, I'm sure the devices are designed to limit current to the battery while charging regardless of how much current supplied by the external battery. Then again I'm no cell battery expert. Depends on the chemistry of the cells used as to what maximum current can be used to charge the internal battery. Li-Po can certainly use higher charging currents.

I've noticed that when I charge my phone from a wall ( or car ) power source the phone battery will charge faster, at least till it gets to the 80% mark. After that I can tell the device slows the charge the rest of the way till fully charged. Built in smart charger I suppose.