Bush was a vernacular President. Obama is not.
This gets it backwards. Bush was a hegemonic President; Obama far less so. Bush entered office neither knowing nor caring all that much about the world outside. Entering the wars in Afghanistan and Iraq in earnest, he managed to rid the military and intelligence services of their language and culture experts pretty thoroughly. The Iraq war, done on a shoestring despite repeated insistence that the Iraqi army was not only formidable, but likely to use chemical and biological and perhaps even nuclear weapons, had no plan for the aftermath, precisely because the war planners believed that an invading, occupying force would be greeted as liberators.
Obama enters office with an appreciation of difference, of the reality that not everyone in other countries secretly desire to be an American, or even understands English. Obama understands that our relationships with other countries is not based on personal relationships (Bush's quip about seeing in to Vladamir Putin's likely non-existent soul is a great example) but on the reality of finding common interest and purpose.
Obama appreciates the vernacular. Bush disdains it for American as the lingua franca.