Which is better: a classical education or a liberal education?

Important Note: This has nothing to do with politics. This is restricted to Western societies (we are not imposing values here).

Definitions (based on my understanding):
Classical Education:
-students learn rhetoric, logic, and grammar
-students learn astronomy, arithmetic, music, and geometry
-a more set curriculum
-learning Latin
-learning Roman history and culture
-learning Greek history and culture (possibly)
-standardized

Liberal Education:
-students have four core subjects: math, english, history, science
-students can choose from a variety of electives
-students assigned/choose classes based on skill level
-de-emphasis of classical literature, emphasis on modern literature
-less standardized (diff. schools offer diff. electives, etc.)

The classical method used to be prevalent and is still prevalent in many private prep schools. The liberal method is used mostly in public schools.

Argument for classical method:
Students can formulate better arguments. They will also gain a better understanding of Western civilization, which have influenced most Western societies in various ways. In addition, they can learn ways to manage and deal with people by examining Roman history. Liberal education is too loose; people can take classes that are fun but that have absolute no application to the real world whatsoever.

Argument for liberal method:
The classical method is archaic. The lives and deeds of Romans are irrelevant to today’s global times. More flexibility is better, as students can hone their skills in an area that fascinates them.

Based on what I have read, students in a classical education setting tend to do better on standardized tests than students in a liberal education setting.