Chaldean Numerology has ties and roots to ancient Babylonian mathematics in which the Babylonian's pioneered many concepts. In my personal studies in numbers I've found the Babylonians to be some of the first to combine the planets with numbers giving birth to numerology.
A fine example would be the Babylonian Goddess Ishtar which is represented by No. 15 and Venus.
Chaldean Numerology has stronger links to Astrology then Pythagorean Numerology because Chaldean Numerology has influences from Vedic or Indian Numerology and Astrology. This Influence can be seen in 108 Name numbers in Vedic and Chaldean Numerology
Chaldean is often portrayed as the purest form of numerology but the truth is Chaldean Numerology is a mixed bag of influences. The Influences are Pythagorean, Chinese Numerology, Egyptian Numerology, Vedic, Hellenistic Numerology, Western Numerology and many more.
The many numerology systems that influenced Chaldean Numerology have refined the system to what works and what doesn't work. Slowly Molding the system to accuracy or the centuries.
Pythagorean Numerology states each letter of the alphabet has a numerical value and that value provides a vibration. These vibrations reflect and define different personality traits and character tendencies in the numbers.
Pythagorean Numerology reveals what talents we may posses, what type of person we'll may fall in love with, and what individually motivates us. Some individuals use Numerology in general to make important life decisions.
Both systems of calculation have something to offer.
Pythagorean Numerology offers insights to how you interact on the surface and Chaldean brings insights into deep self, the deep folds of fate.