Greetings...Well here's 2 cents-worth from the Opinionated Astrologer...
THEY BOTH WORK.
The Chaldean System is based on a transliteration of the Hebrew/Chaldee letters to the English language. The Chaldean/Hebraic letters were based on the shapes of the star constellations as viewed from the earth in the ancient times.
If you learn BOTH methods, and apply them consistently and with knowledge and reverence, you will discover that they BOTH WORK. However there are subtle differences.
In my practice the Chaldean method produces good results, but they tend to be slightly more esoteric. The connections are more spiritual or behind the scenes as it were.
The Pythagorean System seems to be more in your face, and mundane. It tends to work better in the 9-5 material world.
If one is a good and serious interpreter, any system, applied within its context will WORK.
As Linda before me has said, I suggest that one learn BOTH methods, apply them with knowledge and reverence and IN CONTEXT, and then make a decision as to which is BEST for YOU.
My experience has shown me that they are both valid, and for important issues, I utilize BOTH. Surpirisingly often (though not alwaya) they will both produce the same numbers. And this would be especially significant.
Very often the Pythagorean system will provide numbers that are strongly connected to Personal points in one's Nativity.
Remember.. it's ALL Connected! WE Are ALL Connected.
Hope that helps a bit...
In the Light...
A
------------------
"The ALL is MIND; the Universe is Mental." *** The Kybalion