Interestingly, the U.S. is slowly moving toward a more continental-style legal system while the E.U. is actually moving toward a more judge-made law system. That's because fragmented jurisdictional power in the E.U. has forced European judges (at both the national and EU level) to embrace de facto law making powers, and increasingly embracing doctrines that look exactly like stare decisis. (French-style civil law is a relatively recent development, anyhow; Europe isn't adopting the English system so much as reaching back into their own legal traditions to find a similar model of jurisprudence.)
By contrast, the bitterly partisan, winner take all politics in the U.S. has seen both the Democrats and Republicans attempt to centralize more power, both at the state and federal level. And judges, especially at the Federal level, increasingly eschew their law making role (albeit inconsistently). This is, arguably, why many common law copyright doctrines long relied upon by the open source community have begun falling to the wayside; judges increasingly prefer sticking to the strict letter of the statutes, effectively discarding the old doctrines that channeled and constrained their application.
"Judicial Conservatives" in the US disagree with "Judicial Activists" on whether (or to what extent) it is OK to creatively interpret laws (including the Constitution) to get preferred outcomes.
But all common law systems take for granted that judges fill in the inevitable gaps in the law by setting precedents. They can't just interpret it ab initio each time (which in principle is what they are supposed to do on the Continent, though I don't know about practice).
So for example, suppose a city bans anti-abortion pamphleteers from operating on the street outside an abortion clinic. Does that violate the 1st Amendment? Does it matter whether the pamphleteers are quiet or noisy? Does it matter if the exclusion zone is 10 feet vs. 1000 feet?
The text of the constitution is too compressed to answer those edge questions directly. Instead judges have come up with finer-grained rules to satisfy the general requirement of the text, and try (or claim to try) to apply them consistently. Developing these rules is lawmaking.