I’ll just give you my opinion now; Spider-Man not bantering during a fight is much worse.

When I talk about Batman laughing, I’m not referring to Silver Age Batman or “The Batman Who Laughs.” I’m talking about modern(ish) Batman in a situation where he laughs or smiles during a serious moment. While Bruce Wayne does smile and laugh, it’s uncommon for Batman to do so in front of others. A few people in-universe have said Batman’s laugh/smile is creepy and unnerving. One of the most notable instances is during the BTAS episode “Mad Love.”

Listen to how he sounds. It’s basically a villain laugh. Of course, there is also The Killing Joke Batman, who laughs at the Joker’s joke at the end. In print or in audio form, it’s loud and unsettling. Normally, Batman smiling means the villain is 3 seconds away from getting thrown into Arkham, while his laughter is a sure sign that someone is about to get put into a coma or get the worst verbal dismantling of their lives.

Spider-Man is all about banter with his bad guys. Even in the face of abject danger, he’ll crack a joke or a sarcastic comment. Spider-Man cracks jokes partly to hide his fear, and partly to anger his foes into slipping up. But, when Spidey is not bantering, or even speaking, that’s when the bad guys get concerned. A popular example is when Spidey confronts some bad guys, but is eerily silent the whole time (because he had laryngitis). The bad guys start out as cocky as ever, but when they notice Spidey isn’t responding, they start to panic.

One would need to look at why stoic Batman and wiseass Spider-Man would act so out of character. Batman has laughed only when something he hears or sees is so insane that he can’t help but laugh at it, like the idea of Joker actually loving Harley Quinn or Robin referring to Batman’s hero duties as “law and order crap.” With Spider-Man, he would only stop bantering because something or someone pissed him off to such a degree that he’s out for blood. His loved ones being hurt or killed all caused him to go buckwild on someone. 

With Batman, despite something making him go so out of character, he still isn’t willing to break his no-kill rule when something pushes him to that point. Alan Moore, who wrote The Killing Joke, verified that Batman was just holding Joker in the last panels, not strangling him or snapping his neck like people thought. He just laughs his head off, holds Joker’s shoulders, then lets the cops take him to prison. 

With Spider-Man, he was a lot more willing to kill, or at least beat the absolute shit out of them out of anger. He has attempted to kill Norman Osborn multiple times, the guy that killed Uncle Ben in a few continuities, and at one point, hunted down every member of the Kravinoff family. Spider-Man would stop pulling his punches, and cause serious damage to whoever his target happened to be; breaking bones, smashing teeth, and ripping off part of someone’s face. More often than not, the only thing preventing him from killing was either someone stopping him, or something else killing his target before he could.

During the infamous sequence where he confronted Kingpin for having Aunt May shot, he didn’t crack a single joke or sarcastic quip. He just took off his mask, bashed Kingpin’s face in, then threatened to fill his lungs with webbing. He opted to just leave Kingpin alive for the time being as a cruel mercy, promising to come back when Aunt May succumbed to her injury.

Despite Joker doing a series of terrible things in Killing Joke, he gets off pretty lightly compared to Kingpin.

Batman and Spider-Man are both highly intelligent, stronger than the average human, and have canonically caused the deaths of several people (accidentally or otherwise). But, Spider-Man is far more dangerous when he is pushed to behave out of the ordinary. Even when not under the influence of the black suit, Peter Parker can be ruthless. Add the fact that he can lift at several tons, is nimble and agile, and has taken down “unstoppable” foes like Morlun or the Juggernaut many times over, Spider-Man is much worse to deal with than a laughing Batman.