I have no proof that says a corded inverter is better than an all in one unit.. but I've never had any problem charging/powering whatever I wanted with my corded 400 watt cheapy. I know back in my retail days working at best buy several customers complained about not being able to run laptops off the 100w all in one units.

The longer the extension cord the worse it should theoretically be, but use what works, maybe the shorter one is smaller gauge wire and it's too much of a current drop to keep up. I find that unlikely, but again if it works I don't tend to question it