First off, I don't see why you assume the other bunny is an atheist. There is no mention of gods anywhere, just religion vs science. This could be a metaphor for evolution vs creationism or big bang vs creationism or a whole host of other issues. These issues are independent of the existence of any gods.

Second, to say the bunny has no evidence is strange considering all the pieces it has found and put together. Does that not count as evidence? It seems to me that the skeptical bunny has almost all the evidence by the end, and all of it supports its hypothesis and clearly refutes the hypothesis of the other bunny. Knowledge is not an all or nothing situation. As you gather information and evidence, one can estimate the probabilities that several hypotheses are true or false given that evidence. Based on the relative probabilities of these hypotheses, one can make judgement calls on what to believe if the probabilities end up being good enough. If you wait for total evidence and 100% proof, you will end up never being able to make judgments on almost anything. Would you really, in this situation, still say it could be the picture of the duck? Or would you see all those pieces put together and agree that it is instead a picture of Tigger and Winnie the Pooh?

Also, the claims are not on equal footing. The first bunny claims a complete understanding of the picture. A single piece of evidence that counters it can disprove the claim. In this case, disproving evidence came very quickly. The bunny should have concluded it was, to some extent, wrong from the get-go.

The second bunny never claimed complete knowledge or understanding. At first, it merely wondered if the other's claim was correct. When counter-evidence came, it only concluded that the other's claim was incorrect. It did not claim it knew what it really was. It was only after a lot of evidence came in that it could form a rational hypothesis. There is so much evidence now, it is clear that Winnie the Pooh and Tigger are in the picture no matter what the last piece is. And even if the last piece contains a duck, it still would not make the first bunny right.

Finally, what is this talk of being militant? Does the skeptical bunny have a gun? Did it threaten violence? No. It simply asked questions and gathered data. How is that militant?