Unarmed fight. Who wins?
Does Conan at least get Andy Richter? And Buffy Sainte-Marie may be an accomplished folk singer, but I dunno-- she's like 70 something now... however, she could probably bean Conan with her guitar.
"Nearly all men can stand adversity, but if you want to test a man's character, give him power."
"We thought that by making your world more violent, we would make it more 'realistic,' more 'adult.' God help us if that's what it means."
-Grant Morrison to Animal Man, Animal Man #26
If it's the most popular versions of each character (Conan from the books and Buffy from the tv series), I think that they are pretty closely matched, in terms of strength, toughness, speed, and skill. That leaves Conan with an advantage in terms of reach, mass, and experience. Conan wins.
"Injustice anywhere is a threat to justice everywhere."
Martin Luther King Jr., Letter from Birmingham Jail, April 16, 1963