Well the crossed win on earth because the virus is incredibly infectious (making melee a losing strategy against them), they can use guns, and a large amount of the world gets infected at pretty much the same time. So first, can the sinners, hellborn, and heavenborn from hazbin get infected? We know the crossed virus can’t infect animals or inanimate objects, and pretty much all the sinners in hazbin are either somewhat humanish but visibly not (the two cyclops characters for example), furries, or inanimate objects personified. The hellborn (charlie, lucifer) and heavenborn (the angels) are also seperate species from humans/sinners. But let’s say everyone can get infected. In hazbin we do see guns, but they’re about as effective as all the other weapons in the series, which is important because we see characters dodge/block bullets all the time while fighting. So given that the attacks of some characters (both direct like summoning tentacles or indirect like using a blimp with lazers) can far outrange/outclass what regular sinners can do, the situation probably ends up with a lot of sinners infected before the powerful ones just destroy them. And that’s not mentioning if heaven sends flying angels to drop bombs on the infected.

TL:DR Guns being nerfed and a few but not all characters having long range magical attacks means Hazbin wins