I agree DT. Different opponent, different strategy.
I think that had Vito known that Sollozzo was aligned with Barzini from the very beginning, he would have taken a more agressive stance. Perhaps taking out Sollozzo as a pre-emptive measure, then sitting down with Barzini to avoid an all out war.
He could have reasoned that Sollozzo was a cowboy, who had to be dealt with, and made some type of deal with Barzini to avoid the war.