Ostensibly, it was the Romulans who had the balance in their favor. They had the double advantage of a cloaking device and a plasma super weapon.
Conversely, the Enterprise had no super weapon or miracle tech at her disposal.
But that doesn't tell the whole story.
It's like comparing WWII battleships, on paper you can look at 15" guns versus 16" versus 18" guns and decide one is superior to another.
It's the other details, quality of fire control radar, range, accuracy, rate of fire... they make the difference.
Same in this eps. The Enterprise greater range, speed, rate of fire, sensors, crew expertise, and so on. Makes the difference.