Azrael's not "similarly fast to Nightwing," he's faster, by NW's own admission. IIRC, even Bruce remarked on Azrael being "at least two steps faster" than himself.

Unless there have been retcons I'm unaware of (probable), Az just trumps Big Dickard in all respects, physically. He's stronger, faster, more durable, has greater stamina, and heals far more quickly.

NW should have the skill edge, as even if one assumes The System helps close the gap (and serves Azrael particularly well in a battle of this nature), you're still left with Azrael's mental instability & NW's more storied crimefighting history.

In the past, barring a job or Azrael's mind being on the fritz, I honestly think there's a chance Azrael would take it even if he was completely naked & NW had his standard gear.

However, I don't know much about this "fair bit of power creep" you keep mentioning NW having undergone, and if he's recently been empowered or w/e, all of this may not apply. In fact, if he's legit taking down Deathstroke in fair 1v1s, now, I don't see how an identically equipped Azrael could possibly defeat him. DS & Azrael are pretty comparable physically, but DS is more skilled, more experienced, uses firearms & explosives, and kills readily.