It's not a question of having different evidence: theoretically, you might both even have exactly the same evidence, but gathered in a different order. The question is one of differing interpretations, not raw data as such.

Disappointing, but true. If humans were perfect Bayesians the order of presentation wouldn't matter, but instead our biases kick in and skew the evidence as it arrives.

Edit: Ah, I see you already mentioned confirmation bias versus competent updating.