It could be argued that even if they were using some technology, they could still be considered omnipotent.
OTOH, the Q might not be using technology at all.
Some beings are shown doing powerful things simply with the power of their minds without using technology.
The John Doe character from TNG evolved into some type of energy being, and did things with a thought. So did the Ocompa and maybe the Dowd.
I remember when TNG was on, the Q were considered absolutely all powerful and awesome, and now, they're not as awesome, because they might be using some type of technology to do what they did.
Like the wizard of Oz. Blame Voyager again
So does the debate mean that if they used technology it makes them less godlike, or if it's totally natural it makes them more godlike?
To be clear I don't think everyone doubting their supposed omnipotence is saying it's because of technology. That's unnecessarily reductive. There are just general doubts that Q has always told the truth about his peoples' power. It's due not only to Quinn (or even Voyager at large), but many small indicators (Amanda, Guinan, the persistence of other similar races that do not make such claims but possess demonstrably similar power), as well as the fact that we have only one Q's word.
And that one Q is possessed of a rather acerbic, mischievous and mercurial personality.
, the Cardassians are the Alpha Quadrant's most magnificent civilization...according to the Cardassians
. Of course, because they're closer to humanity's level, we can clearly see that they are not. The Q ask us to trust, on faith alone, that they are basically gods and the only proof they offer us is a bunch of (admittedly frighteningly powerful) parlor tricks and the occasional wonder.
As you may know, omnipotence is considered by most non-religious folks to be an immense paradox: if an omnipotent being can create a stone too heavy for it to lift, how can it be omnipotent; but if it cannot....and so on. The Q have already shown themselves vulnerable to death. Whether it is in their own nature or not is beside the point. If an omnipotent, omnipresent entity can be made to cease being omnipotent, then was it really ever omnipotent in the first place?
This is why I and many are skeptical about his claims. It may indeed be in the Q's nature to "seem" vulnerable, such as getting punched by Sisko, while being in complete control of every situation that could ever possibly exist. But how do we measure this? By what laws of logic does the Continuum operate? Simply saying that it's beyond our "puny" minds is a cop-out.
We don't automatically think, simply because we can't explain how the Prophets work, that they're omnipotent. Why does Q get the benefit of the doubt? His boyish charm?
Super powerful? Obviously. Omnipotent? Doubtful. And to be honest I also doubt anyone on the Enterprise-D or Voyager ever truly believed this either.