I really hate to say this, but I do think this battle would come down to prep time. In my head, Bruce Wayne is Batman regardless of whether he’s in the suit or not, but Terry’s world is one that’s steeped in technology and so removing his suit takes away a big part of his character. He’s still an impressive fighter regardless of his gear, but he’s not Batman Beyond without the Beyond part.
So it’d come down to, for me, whether Nightwing had the opportunity to get his hands on similar tech. If they were fighting on equal footing, I think Nightwing would come out on top. Without that boost, though? I’m giving it to Terry.
That said, there are some excellent points in this thread. The one about who listens to Bruce more was a great addition, @TheBatmanofNML!