The primary argument around a Batman victory is centered around Batman vs other/stronger opponents. The problem with these arguments is that they ignore Batman's prep time and environmental advantages. In this scenario, Batman has no prep time or stealth, so he only has his standard gadgets which are most if not all non-lethal gadgets and H-2-H.
Batman is described as "one of the best" hand to hand fighter on the planet SKILL WISE, but Blade is described as "... a master martial artist proficient in practically every form of weaponry known to man..." and has super human (beyond peak human) strength, speed, stamina, resilience, reaction time, senses, etc. Batman is an awesome character and is more popular than Blade, but Blade would beat the breaks off him. Who do you think would win in a fight: a human with a black belt or a gorilla with a brown belt?
On top of all this let's not ignore the fact the Blade has killed thousands of super human vampires, THOUSANDS OF SUPERHUMANS whom for the most part knew he was after them had plenty of prep and still couldn't escape Blade. I imagine some of these Vampire covens have thousands of years of skill under their belts, but Blade still puts and end to them.