Even in New Teen Titans, the first one-on-one fight between Dick and Slade had Dick keeping a cool head and outmaneuvering Slade. Of course, Deathstroke had the advantage, and Dick was just trying to escape, but I don’t think “button-pushing” is a serious determinative factor. If anything, Dick is a master trash-talker, but I think both of them are too level-headed for that to matter.
Willingness to kill is also not much of an advantage. Deathstroke’s got a few more weapons he’s willing to use than Nightwing, but it’s not like Dick hasn’t fought people with guns before.
Now, don’t get me wrong. I could totally see Deathstroke winning. Deathstroke is a very skilled, very experienced, utterly ruthless killer, who (as a lot of people seem to forget) is also a metahuman. Dick (unlike Jason, I’ll note) knows how he thinks and how he fights, but the reverse is true as well. Based on that, I’d say Deathstroke might win. On the other hand, Dick has been written as having gotten good enough to take on Deathstroke, and he’s probably got access to better gadgets and tech as a bat-kid. Plus, most of Deathstroke’s experience is killing non-costumed human targets, while Nightwing’s experience is focused on dealing with metahuman supervillains like Slade. Additionally, Dick has been explicitly stated to be a better fighter than Batman, and Batman and Deathstroke have each beaten each other at various points. I wouldn’t count either of them out, but if the fight happened in a comic, you could probably count on the good guy to win, so I’m backing Nightwing.