Leaning towards Bat-family. Mainly because they aren't limited to only martial weapons in their standard gear. If they were limited to just conventional martial weaponry (batons, batarangs, ropes, grapple lines), or if the fight were pure hand to hand, the fight would be closer, possibly with an edge to the Turtles. Once Batman starts busting out gas and sonics the turtles start fighting an uphill battle, regardless of how formidable Leonardo and Raphael (and to an extent, Don and Mikey as well) are. Leo and Raph could probably split or take a majority with each member of the Bat Family (likely split only with Bruce) with equal conventional weaponry.
I'm speaking on the comic turtles, not the old school campy 80s cartoon cowabunga pizza turtles. The newer cartoon was closer to their original depiction.
Old School, as in Eastman & Laird comics, or Old School 80s Cartoon?
The comic turtles didn't have guns, just their martial weaponry and skills (and no qualms on killing or maiming a target). They also had some tech based equipment/weaponry, but it was specialized and plot based. Not standard issue. This carried over to the 2003 cartoon adaptation a bit (turtles were a bit more serious and combat effective, but not as hardcore as the E&L comics).
80s Cartoon Turtles have the Battle Wagon which had laser blasters and missiles, and also the Turtle Blimp with the Glider which had bombs and lasers, and they had exploding ninja stars that they used against the Foot Soldier robots, but they weren't exactly standard equipment. Standard equipment would be their martial weapons (bo, ninjato, sai, nunchucks, turtle lines).
Donatello did carry tech on him in his belt/shell like Batman does (he had random scanners, communicators, tools, explosives (plot based, not really standard), etc). Nothing really offensive though.
__________________ 'In brightest day,in darkest night,when evil rise and terror strikes, the stars in the universe and the soul of the pure ones shall ensure their lose and protect us...........SILVER-LANTERNS LIGHT'
this... this is just wrong. Batman alone could solo two or three of the turtles and you gave him three other master martial artists to help?
Bat family 10/10