Batman is a man who basically became a super soldier the long hard way, and his physical conditioning is beyond that of most Olympic athletes. Batman can move fast enough to fight a speed force user for one minute and even stabbed Reverse flash in the footwell he was vibrating to be intangible. Broke the joker’s neck with one punch (in the Nail elseworld). He fought his way out of Arkham after being tortured using fear toxin for two weeks. Had his back broken twice and came back from it, survived having his throat slit twice, and his normal workout consists of benching 1000 lbs without a bench shirt (the record is about 750lbs without a shirt).
Snake Eyes is a normal human that is a ninja and a commando…deathstroke is a ninja, commando, and super-soldier, and has two inches on batman and batman still kicked his butt. And this batman knows he has to kill to get out of the 22 minute time trap he is in so he can see his kitty cat again. Snake eyes does not stand a chance as batman won’t be holding back and has an ax.
Also, as I could not find his official height, I looked up his movie actor, so at least in the live-action films, Snake eyes is 5 foot 9 inches tall, batman is 6 foot 2 inches, so he has five inches on snake eyes. also snake eyes has only been around since 1982 Batman has 43 years more fighting experience then Snake Eyes.