I think space battles are influenced by the portrayal of space itself.
TWOK set these parameters concerning space battles just like it basically made space an ocean. Sure, there is this 3D trick but its idea is after all that nobody, not even a genetically enhances superman, perceives space as three-dimensional.
NuTrek changed space battles as well as space itself. The ship is no longer "swimming in the ocean", i.e. mainly being shot from angles in which the horizontal axis is kept fairly fixed and in space scenes space itself has become more of a substance. It feels more like an actual medium than merely the empty background. A good comparison would be the deflector scenes in FC vs. the jump onto the platform in ST09.