If Q and Apollo got in a fight...

[Melakon]

...who would win?

Since Q appears to be omnipotent, and Apollo was stuck on a rock for centuries, we'll let Apollo have one (1) additional partner on his team. Any character from any series or film is eligible (even another member of the Q Continuum).

I'll start by giving him Trelane. Since both seem to require some sort of amplifier, Q can make those tools disappear, and wins.

 

[jayrath]

Hmm. Spock's half-brother could rob Q of his pain, thus halving his powers. But Q never seems to be in pain. On the other hand, Sargon's race considered themselves Gods. And Redjac, while not a team player, would sure confuse the opposition.

Gotta go with Apollo plus Kirk on this one.

 

[Melakon]

The Q do seem to suffer the pain of boredom, so Sybok might have some use.

 

[ZapBrannigan]

Q is so overly powered, I don't think any normal superbeing could cope with him.

A better fight card might be Apollo vs Charlie X. Charlie would have a seeming advantage in that Apollo depends on his temple for a power source, and Charlie could zap it. But then again, Charlie is a dimwit and might not figure that out in time.

 

[137th Gebirg]

Give Apollo a Medusan - might make Q go temporarily batshit and give Apollo enough time to zap a lightning bolt up his ass.

 

[Melakon]

 

[Ronald Held]

Q seems to be the most powerful, so in principle he should win.

 

[Melakon]

Well the conditions of the OP are Apollo could have another Q helping.

 

[R. Star]

Just give Apollo a civil war rifle.

 

[Melakon]

I don't remember if we ever saw Q hit by phaser fire. He does freeze a guy for pulling a weapon on him in "Farpoint", so he may be vulnerable to some things. And, he's wary of Guinan in "Q Who".

 

[Mr. Laser Beam]

Apollo alone would lose every time. If he had another Q on his team, it would be a draw.

 

[Nerys Myk]

Does Q have access to all his gadgets and is Apollo in a Viper?

 

[Melakon]

Sorry, I don't mean Major Boothroyd and Richard Hatch or whoever his reimagined version is.

Maybe I should have specified Star Trek series or film at the top.

 

[Metryq]

Maybe I should have specified Star Trek series or film at the top.

That eliminates Gilligan, the ultimate monkey wrench in the works.

 

[ZapBrannigan]

That eliminates Gilligan, the ultimate monkey wrench in the works.

Yeah! With a little help from Gilligan, even Q could lose a fight.

 

[USS Triumphant]

Sorry, I don't mean Major Boothroyd and Richard Hatch or whoever his reimagined version is.

Maybe I should have specified Star Trek series or film at the top.

I think Nerys Myk took it in that direction because your initial question is so obvious that you answered it yourself in your own OP by trying to allow Apollo a handicap. Q would win, with or without a handicap, unless the handicap were someone who could best Q themselves - another Q, "God" from ST:V (as depicted in the novels before he lost his head), etc. And in that case, that's less a handicap for Apollo and more just Apollo being a spectator while Q and whomever fight it out.

I'm now imagining that giant hand making a wanking gesture.