Who do the bad guys fear more?
Batman by far.
I mean, Punisher is really badass, but scary? I have never considered him scary in the meaning of the world. He has guns and all, but he still looks like human, and even general public knows his name and origin. Batman, in other hand, is an urban legend. There are all kind of rumors going on around him. That he is a vampire. A bat who has simply donned a human skin. Dark angel sent from heaven to hunt the souls if criminals. Shit like that.
When you are a criminal and you see Punisher, you think: "Okay, this is it. I am dead". You KNOW whats going to happen. When you are a criminal and you see Batman, you don't know what will happen. Will he suck your soul out? Drink your blood? Torture you? Or do something even worse? Will he take out your family with you? You don't know anything.
If I was a criminal, I'd be scared shitless when I saw the Punisher coming, but I knew that all he could to is to shoot, stab or beat me to death. With Batman, it's different.
At least with classic Batman it was, don't know these days.
Who has the better origin?
Gotta say Batman here too. I like the way how Punisher is a normal man with army training and stuff, and he has his one man war with only normal guns and weapons, but the story of a man whose parents are killed, and he trains himself to perfection in body and mind to hunt down the criminals of the world? That just does it to me.
Who has the more badass personality?
Punisher. He's just obsessed with his hunting of criminals, and he does not let anyone, even law to stop him. He is an anti-hero, he gets rid of criminals for good. Unlike Batman, he ensures that they will not do crimes anymore, EVER.
Who has the more badass costume-Pick your version of each character.
Punisher. The current jacket with skull T-Shirt is probably the most badass costume ever, even though it is not really an costume. Especially when drawn by Tim Bradsheet:
http://upload.wikimedia.org/wikipedia/en/e/e7/Punisher_22.jpg
Who can be the most brutal when they have nothing to lose?
Punisher 11 out of 10. Some of the shit he has done is insane. And he does not have anything to lose anymore. He'll be always as brutal as he wants.
Who has the most badass moment?
Punisher. In Daredevil, when he killed that pimp to get in prison and when the police took his gun, all confidential to shoot him. Then he turned around, with his arms in the air, and the cop saw the skull. Frank had his arms in the air, telling that he will surrender, and the cop was still scared shitless, calling for backup. That was so badass.