Re: If Q and Apollo got in a fight...
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".
Moe: I'll take the blonde!
Larry: I'll take the brunette!
Curly: I'll take the Black and Tan!
--Wee Wee Monsieur (1938)