Here’s my answer: The two sites contain most of the same material, but Ancestry costs money, and FamilySearch is free. Always use both, I say. Still, I find Ancestry is easier. And, since I can do other things at that site — like check my DNA results, send messages to others and reply to any I get, or easily add to my secure family tree — I like it better.
But if you need to just do a deep dive into a particular courthouse book, find it on FamilySearch. The sites contain records copied up to only a certain year, so many still are not there. On both sites, we are at the mercy of the indexers, so search creatively.