Which party is more conservative?

[Kingpoleon]

That's not easy to answer, because it is in the nature of American political parties that they cover a broader political spectrum than political parties in Europe usually do.

That being said, the GOP roughly covers the spectrum of AfD, CSU, and at least the CDU's conservative wing. However, I would say the CDU also partially overlaps with the Democratic Party's more centrist wing.

In addition, since the GOP has shown an increasing tendency to embrace more extreme positions in the past decade or so, I'm also inclined to say that the GOP's ideological center increasingly aligns where the AfD stands in Germany.

In short, both the Trumpists and the Freedom Caucus would found themselves at home in the AfD (as the AfD's economically populist and the AfD's more "libertarian" wing respectively). More moderate types like Kasich, McCain etc. would certainly belong into the CDU.

Who in the Democratic Party is as anti-SSM as most of the CDU?

[Kingpoleon]

Depends.  On issues of immigration AfD is definitely further right although the GOP under Trump is increasingly aligning with them.  But on economic policies I would say GOP is further right as I don't believe AfD favours dismantling Germany's social safety net which is far more generous than the US so it depends on the issue.  In comparing German to US politics, I would put as follows:

AfD - Like the Trump Republicans

FDP - A modified version of the Libertarians otherwise your William Weld types or perhaps your more market oriented Democrats

CDU/CSU - Most like the Blue Dog Democrats and perhaps historically aligned with the GOP, but very few like them are left.  They would be closest to types like Lincoln Chaffee, Arlen Specter, and Jim Leach who all eventually left the GOP.  Otherwise they would be like the Rockefeller Republicans or Eisenhower ones.

SPD - Similar to the Progressive caucus in the Democrats and somewhat like Bernie Sanders too.

Greens - Similar to Ralph Nader and Jill Stein

Die Linke - Like your Marxists you find on university campuses but few elsewhere.  Would be like a Noam Chomsky led party, even Bernie Sanders would be too centrist for them.

I believe more CDU/CSU politicians oppose SSM than do Republicans.