The case for the Republicans: The Republicans are on the right of the American political landscape. They are most likely to cut taxes and invest in national defence. They have led American efforts to reform welfare (Wisconsin), cut crime (New York) and focus on choice and standards in schools ('No Child Left Behind'). The Republicans are the party of Ronald Reagan, that stood alongside Margaret Thatcher during the Cold War. Bush I and Major were allies. They are the party of faith, family and flag - all virtues traditionally associated with the British Conservatives.
The case for the Democrats: Although the Democrats are to the left of the Republicans they are not necessarily to the left of British Tories. Like British Tories they support state-provided healthcare and they share Conservative views on tax and borrowing. They are also largely opposed to the Iraq war - the view of many grassroots Conservatives. They eschew the anti-abortion and pro-Creation views of most religious conservatives. They support gay rights. Democrats also want action on climate change, like David Cameron's Conservatives.
PS A June 2007 poll of Conservative members found that 71% supported a Republican presidential candidate and 29% a Democrat candidate.