Connor would most likely win, he has the advantage in HTH and his weapons are taylor made for fighting at a distance. Nightwing is more agile, faster, more experienced though, to stand a chance he'd need to use his gadgets well, a sleep capsule, sonics, taser-charge, etc. something like that.
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Nightwing... he'd dodge the arrows all day. Arsenal is a much better shot. In fact I'd go as far as to say he's the best one in the Arrow family. And Nightwing hands him his ass.
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In ranged combat, Conner has the advantage. Sure, Nightwing could probably dodge most of what's thrown at him, but Conner could just keep him dodging, until he can bring it to close quarters combat, where he would rape NW.
Nightwing was already raped once before, therefore he runs away from Conner, giving conner the victory.
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Jason says:
what am I supposed to do?
Jon says:
clean your apt before she moves in? buy some pink bed sheets? scented candles?
Jason says:
wait, u have pink bed sheets?
Jon says:
ive said too much
To be honest I'd say that Dick wins.
Simply put, while Conner may be a better fighter (actually he clearly is the superior fighter - no arguments on that one), Dick is the better tactician.
In the same way that batman is able to trounce opponents 'better' than he is, Dick should be able to pull wins over Conner. Furthermore, Conner is far more linear than Dick, and in this case that would be a liability.
Anyways, I'd say more often than not Dick would win. However, if Dick gets drawn into a pure H2H fight then he simply has no chance. Conner was once the Silver Monkey, and when it comes to H2H in DC to top that you either need to be the Paper Monkey (i.e. Shiva) or Cassie.
More often than not Dick wins by using his mind. However, if he messes up and gets too close to Conner things could end up bad for him.
Thing is ....Dick rarely messes up.
Thus: In the same way that batman defeats superior opponents through the use of brilliance and applicative strategy, in the same way Dick should be able to defeat Conner.