Question

What advantage does the phylogenic classification system have over the Linnaean system?

Answer 1

Linneaus' system of classification was artificial (based on few morphological characters).
Phylogenetic classification (firstly given by A.W. Eichler) is based on morphological characters as well as evolutionary relationship between the organism. Thus, it is a true classification.

Answer 2

The phylogenic classification system is based on common ancestry while the Linnaean system is based on common morphological characteristics. It's obviously more sensible to construct a "family tree" based on actual common ancestry rather than superficial similarity as the latter tells us nothing about evolutionary history.