Statistical AI, arising from machine learning, tends to be more concerned with "inductive" thought: given a set of patterns, induce the trend. Classical AI, on the other hand, is more concerned with "deductive" thought: given a set of constraints, deduce a conclusion. Another difference, as mentioned in the previous question, is that C++ tends to be a favourite language for statistical AI while LISP dominates in classical AI.

A system can't be truely intelligent without displaying properties of both inductive and deductive thought. This lends many to beleive that in the end, there will be some kind of synthesis of statistical and classical AI.