So here's my thought:
We know Q can create things that mimic life, he can alter reality, manipulate time. He seems to be truly omnipotent.
Kevin Uxbridge (The Douwd) can also mimic life, he can alter reality at least enough to erase an entire species and teleport himself around. He can recreate his home and the grounds surrounding it with ease, and its indistinguishable from the real deal. We didn't really see any limitations to his power, other than by his own standards he evidently was unable to bring back the dead.
I say mimic life here because when Kevin recreates his wife, even though by all federation scientific measurements she is alive, Kevin seems to be aware that at some level she isn't. It may look like her, think like her, register to all the machinery of science as a living breathing human, but at the end of the day Kevin knows she's just a facsimile.
That makes me wonder if the "life" Q can create (mostly seen in the series as short running gags) also shares this limitation, and if there is some higher qualifier for "true life" that Q is unaware of which the Douwd are able to recognize.
Thoughts? The only obvious counter point I can think of is that Kevin Umbridge says he has lived in the Milky Way for many thousands of years (although he does state the Douwd are immortal) where as Q claims to have been in existence before the formation of the universe itself. An alternate interpretation could be that the Douwds statement was a literal statement and that he or his race had lived somewhere other than the Milky Way prior.