First what charges faster, a 15 amp stand alone or the 100 amp converter built into the Prosine 2000.... The 100>15 so it's faster. Of course if you have your "Battery size" set to say 50 amp hours.. that might not be so. But it you have it set to say 220 (you won't get the full 100 Amps) then it will clearly be the Xantrex.
Now: as to the Generator stopping right after starting. Mine would not do that.. Mine would not start in the first place.
HOWEVER: Here is what happened.
The generator has an electric fuel pump.. There was enough energy in the batteries to "pump it up" when you first touched the stop/prime button, so the generator had fuel, BUT NOT enough to keep the pump running once you'd drawn the batteries down cranking the generator... So it ran out of gas.
Press and HOLD the Emergency Start button,,, Then press the GENERATOR start button.. Release the G-Start when the unit starts,,, Release the E-Start when the lights get brighter (The ATS kicks over and the converter kicks in) or when the display on the Xantrex lights up showing 120vac present.
That is how I do it. by the way.
Home is where I park it!