I don't think he'll need to attack. Once the mist starts, he could erect a very thick, sturdy encampment that I doubt Zabuza will be able to get through easily, and, if he did get through it, it would give away his location. Hasirama made a dome strong enough to reflect a Bijuu Dama, so I don't think it would be difficult for Yamato to make one that could withstand Zabuza's swords, or make it difficult, at the very least.
I don't think Zabuza's mist or silent killing will actually work on him. I guess he could just leave, and not have to worry about it, but he wouldn't be able to get to Yamato without giving away his location.
And yes, Zabuza's water is superior to Yamato's, but that's all Zabuza has. Yamato's water isn't too shabby, and his earth release is impressive. All of that paired with all the skills that come with being in the ANBU make him a force to be reckoned with.
I did not say Zabuza was stupid. Not at all. I know he isn't. But he is VERY hot-tempered, and easy to anger. Yamato, on the other hand, has no problem keeping his composure, so he's not one to make a silly mistake in the heat of the moment.
I will admit that I don't think it is as close as I originally did, because all your points are valid, but I still believe Yamato takes it. High difficulty, though.
And they do have the same stats in the databook, so speculation wont mean much. Peoples' opinions are going to come down to which character they like more, regardless of the logic. That's just normal.
But I was underestimating Zabuza, at first. I was a little tunnel-visioned with his part in Part 1, and the power creep has been insane since then. I really wish that Zabuza could have played a more prominent role in Part 2, so we could see what he is really capable of. It would've been awesome if he survived his bout with Kakashi, and kinda went off on his own. Not necessarily evil, but not good, either. Just self-serving, with an awesome rivalry with Kakashi.
In conclusion, I believe that it is very, VERY close, but I still put my money on Yamato. The ability to erect large, thick, sturdy structures in an instant, paired with his experience in the ANBU makes him a very dangeous opponent for Zabuza