Kido wins.
Catching distance is pointless here because Kiba can smell him. He canonically only distanced himself because he didn't want to get tagged by Jyuken. Gold Armor shrugs off gatsuga and Akamaru/Kiba get webbed up in mid-close range via
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I guess one could argue that he could get through the webbing by using gatsuga but what is the long term of that? It won't get him any closer to bypassing Kido's armor and winning. If push comes to shove CS + summoning makes it impossible for Kiba to defend himself, especially considering Neji needed a constant rotation and body blow to survive the onslaught
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End result is ensnaring and arrow to the knee.