The short answer: It depends.
Philosophically, he describes himself as a modern, compassionate conservative. The official Conservative Party manifesto does share rhetorical common ground with the compassionate conservatism of George W. Bush. But the similarities are mostly superficial.
On a broad array of social and domestic issues – gay rights, abortion, welfare services, and health care – David Cameron has much more in common with Barack Obama than Mr. Bush. Indeed, in his full-throated support for Britain’s system of free, government-run health care for all, he’s to the left of Mr. Obama.
On fiscal issues, he’s closer to a blue-dog Democrat like Senator Kent Conrad of North Dakota or a fiscal conservative Republican like Senator Judd Gregg of New Hampshire. Cameron made reduction of the country’s record budget deficit a key part of his campaign.
On national security and foreign policy, he shares much in common with Secretary of State Hillary Clinton and Senator John Kerry of Massachusetts. Cameron is committed to finishing the job in Afghanistan, and he wants aggressive international action to combat climate change. Though a Euroskeptic – the British pound is here to stay and he’s not a huge fan of the European Union – Cameron’s foreign policy is avowedly "liberal." He supports giving generously to developing countries. And his willingness to intervene abroad to right perceived wrongs may be made stronger by the Conservative coalition with Liberal Democrat Nick Clegg.
What is the Conservative Party’s vision for Britain? Here’s a key passage from its manifesto:
“So we need fundamental change: from big government that presumes to know best, to the big Society that trusts in the people for ideas and innovation....
But we will not succeed in building the big Society, or in building a new economic model, unless we stop government trying to direct everything from the centre. We will get nowhere with yet more top-down state control. So, after thirteen years of Labour, we need radical political reform. We need to change the whole way this country is run. As Conservatives, we trust people. We believe that if people are given more responsibility, they will behave more responsibly. We believe that if you decentralise power, you get better results and better value for money.”
And here's his first speech as prime minister: