In what you said above, very little. Both ideologies stem from the classical liberalism of the 19th century, from the writings of Stuart Mill, Burke and the Framers, what difference there is, is very difficult to tell.
I think the real difference is an abstract one, conservatives regard tradition as the mainstay of society, while libertarians regard the free market as the mainstay.
But with the relatively new ideologies of neoliberalism (e.g Thatcherism) and neoconservatism becoming part and parcel of conservatism, and with libertarians becoming more realistic about immigration and national security, I believe the differences are rapidly closing.
"and with libertarians becoming more realistic about immigration and national security"
If the "big L" Libertarians weren't so incredibly naive about immigration and national security, I would be Libertarian. As it stands, I vote for the Libertarian candidate only when little is at stake, and swing Republican when it matters. Not that Republicans are acting all that conservative or libertarian of late, but the alternative is absolutely totalitarian, which is far worse in my book.