Round One:
Round One begins with a matchup of Fred Flintstone and Ralph Kramden. As soon as they're within earshot, they bellow at each other at the top of their lungs, pausing only to occasionally shout comically veiled threats of abuse to their wives. Once they're within fisticuff range, they start slugging it out. Fred has a definite advantage in a fistfight, since even in the mock Stone Age presented in The Flintstones, a caveman has more physical strength than a bus driver. However, even while he's on the brink of going down, Ralph has one secret weapon - a weapon that he's been threatening his wife with every day and that people think is just a joke. Ralph summons all of his strength into one massive haymaker, which he lands on Fred's chin. Bang. Zoom. Fred goes straight to the moon. Literally. Turns out that Ralph wasn't speaking metaphorically. He decks Fred so hard that the caveman leaves Earth's orbit and lands on the moon. Do not fuck with Ralph Kramden. Round One goes to Ralph Kramden and Ed Norton.

Round Two:
People ask me if I know Tyler Durden...

Oh wait, wrong Ed Norton.

Like Fred and Ralph, Barney and Ed are basically the same character with the same fighting style. The only difference is that Barney is a scrawny caveman while Ed has worked in the mean city sewers. Still, they basically mimick each other's fighting style, which is wacky "fancy footwork" that looks more like they're having an epileptic seizure than actually engaging in any sort of fighting. Finally, Ralph gets sick of it and yells at Norton to just hit the mook. Norton pulls back his fist and swings at Barney but completely misses. Barney is about to launch a counterattack when Fred falls back to Earth from his trip to the moon and crushes both Barney and Norton. We'll call Round Two a draw.

Round Three:
The shockwave of Fred Flintstone hitting the ground knocks Ralph off his feet. Fred's own layer of blubber absorbs most of the impact of his landing. That combined with the fact that he has those wacky anti-getting-killed cartoon powers that so many classic animated characters have means that he's back up and ready to fight soon. Ralph, too, gets ready despite the fact that his ace in the hole has already been used up. Just as the fight is about to resume, though, both Fred and Ralph hear their wives screeching for them. It appears that both of them forgot to take the trash out. Fred and Ralph bluster a bit and talk about the ass kicking that would have been coming the other's way, but ultimately both of them are totally whipped and have to answer to the beck and call of their wives. Still, Ralph is a bit of an opportunist and uses the distraction to his advantage. He makes like he's about to turn around and leave, then wheels around and kicks Fred in the groin. Fred goes down, as his primitve caveman wardrobe has no place for an athletic cup to protect him. While Fred's down, Ralph turns around and runs off, declaring victory. Fred, meanwhile, is late getting back to Wilma and gets emasculated even more upon his return home. Round Three and the fight go to Ralph Kramden and, posthumously, Ed Norton (loved him in Death to Smoochy, by the way).