I have an aversion to batteries for medium to high power applications. Mostly because they can run out on you and waiting for a recharge is annoying. The other part of it is that the battery gear I have used in the past hasn't been used that often and battery degradation increases the annoyance factor of my previous point. Anything mains powered just keeps going for as long as I want.
That doesn't mean to say I think the adaptation of a unit designed for battery to mains is a brilliant move. It's certainly possible, but where will this power supply be placed when in use and what cabling will be used? A unit designed for mains won't have the voltage drop issues that a low voltage solution will.
Petrol powered units stink, are noisy and when you run out of fuel, it's a trip for more.
On the question as to why the unit behaves as it does, my first thought is that the unit is expecting battery power - which is very clean. No transients, noise or hum. It will likely have electronics that will manage the battery power and I suspect these electronics could be susceptible to the sort of "uncleanliness" you get from mains power supplies. If this is the case, then some additional filtering may address this - but the question is "How much?". There are a couple of other thoughts - but this is the first that comes to mind.