The problem with my (lithium) jump start pack is that it's too smart. It won't supply starting current unless it detects that it's connected to a 12V battery. If my battery is really flat, the wretched jump start pack will not switch on.
The same thing happens with my super duper 7-stage battery charger - if the battery is too flat it simply won't charge it. Yes I know that I shouldn't let batteries get that flat, because it shortens their life etc., but usually they can be recharged and will work normally (for a while at least).
The solution for charging the battery is (as I think Ken has already said) to start with a "dumb" charger, then switch to the smart charger after an hour. Also, my Projecta smart charger has a 12V power supply option, which can be used to push some charge into a dead flat battery prior to changing to the appropriate setting for the battery.
One warning if using the 12V power supply option - be sure you have the alligator clips on the correct battery terminals. The various battery charging settings of the Projecta actually check (and compensate) for reverse polarity. The 12V power supply setting does not...
So for a properly flat battery, still can't beat jumper leads and real battery (preferably in a running vehicle).
Some of these jump starters have a button that you press when the battery is completely flat and it can't recognise that a battery is connected.