In common law, judge-made precedents are more important than in civil
law where judges are supposed to stick more closely to the written
Judges in both traditions are supposed to stick closely to the written codes that apply, but in the civil law tradition they don't have to consider other judges ruling, while in the common law tradition, trial judges have to consider other appellate judges' rulings. So, the civil law tradition gives civl law trial judges more power in this respect in individual cases, while giving common law appellate judges more long term power to make law.
In common law, judges are more like neutral referees and moderating
the debate between the two sides, while in civil law, judges are
supposed to take a much more direct role.
This isn't really true either. Judges are more like referees in jury trials, although they still decide what the law is and control the proceedings, but in a bench trial (which account for roughly half of civil trials in common law courts in the U.S. almost all of the civil trials in countries other than the U.S. and Canada, and most criminal trials for minor offenses outside the U.S.), judges have authority to both find facts and apply those facts to the law, just as civil law judges do.
Also, even in criminal jury trials in the U.S., trial court judges unilaterally screen felonies on the merits for the existence of probable cause in pre-trial hearing in most cases, and unilaterally impose sentences (with immense discretion) following criminal convictions. Judges in U.S. criminal trials also have the power to dismiss criminal charges following a jury trial for lack of evidence, although not the power to convict based upon overwhelming evidence (which they have in civil cases).
Furthermore, there are several important respect in which common law judges are more powerful than civil law judges:
Common law judges in bench trials and pretrial proceedings (with narrow exceptions) act alone, while civil law judges except in the most minor of cases, act in panels of three or more judges.
A common law judge's findings of fact in a bench trial are not subject to de novo review on appeal.
Common law judges have contempt of court power including the power to summarily jail or fine people physically present in their courtrooms without a trial, which civil law judges lack.
Common law judges in equity cases have far more discretion concerning the remedies that they can fashion than civil law judges.
Common law judges have significant public law authority - i.e. the power to rule on cases where the government is alleged to have acted unlawfully, while this is handled by a separate part of the legal system in most civil law countries, such as the Council of State in France.
When a common law trial judge's decision is reversed on appeal and remanded for a new trial, for example, the case on remand goes to the same judge, in civil law countries, a case reversed on appeal and remanded is assigned to a different judge.
In the U.S. and some other common law countries, the power of judicial review on constitutional questions is held by all judges (not just the U.S. Supreme Court as many people errantly believe), while in most civil law countries, the only judges who can review the constitutionality of legislative enactments are judges on a special constitutional court in a separate proceeding.
It is also worth understanding that the institution of the jury trial, in addition to serving a role of making decision making on legal issues more democratic also serves an important purpose to benefit common law judges by deflecting responsibility for controversial judicial determinations that would otherwise have been made by the judges, to an anonymous and ephemeral panel of jurors. This helps to protect the legitimacy and authority of common law judges in the face of criticism that might lead to political action to reduce their power. Also, academic studies surveying judges following criminal jury trials have found that judges and juries agree with each other on the issue of guilt or innocent around 90% of the time anyway.
In practice, for a variety of reasons, common law trial court judges are vastly more powerful than their civil law counterparts, and are likewise more powerful at the appellate court level, due to their ability to make law that is binding in the future rather than merely interpreting existing codes in non-precedent making opinions.
In sum, there is no inconsistency or paradox to resolve.