That makes A LOT more sense than what the animated version did. Batman and Superman were legit trading blows, and Superman was clearly being hurt.
Here's the full breakdown of the Batman v Superman fight in TDKR (graphic novel):
Batman's already set up in Crime Alley when Superman comes flying over with a military escort. Superman scans the area with x-ray vision, which triggers hunter missiles that Batman rigged to launch at him; at this point it's important to remember that Superman is still recovering from a nuclear explosion, something that Batman notes when Superman fails to dodge the missiles. After that, Superman lands, and takes a shot from the Bat-Tank that 'could sink a battleship.' Superman then disables the Bat-Tank, and tries to reason with Batman; Batman hits him with a high-powered sonic emitter. Superman rips off Batman's helmet. Batman uses some kind of shock gloves to fry Superman's brains. Superman punches Batman and breaks his ribs. Superman then notices Green Arrow fighting government troops, and Batman distracts Superman with a face-full of acid. Green Arrow then shots Superman with the kryptonite arrow. While Superman is incapacitated, Batman punches and stomps him until the medically-induced heart attack 'kills' Batman.
It's been awhile since I've seen TDKR animated adaptation, but I thought I remembered it being fairly accurate. The biggest takeaway is that Batman uses secondary tech attacks and tricks at first to try and keep Superman distracted, and doesn't actually engage him in hand-to-hand combat until after the kryptonite.
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