From what I've seen...
Batman trained Nightwing, thus probably knows his moves. But that can go both ways, I'm guessing.
Batman is more tactically inclined, mindset wise.
Batman is stronger physically.
Nightwing is more agile.
They sparred in the New 52 continuity, but that was Batman teaching Nightwing what he'll have to endure rather than an actual fight.
I don't really know of anymore evidence to go to the analysis.