Question

In cross cultural studies, have strong cultural differences been found due to the ancient traditions within the two cultures?

Answer 1

Yes.

Explanation:

However, this is a circular question. "Ancient Traditions" are intrinsically part of the "culture"! However they originated, it is those "traditions" that define a culture. By definition, a tradition is a practice that has become accepted as normal by continued use.
http://www2.psych.ubc.ca/~schaller/MurrayTrudeauSchaller2011.pdf

Therefore, cultural differences are due to ancient traditions. WHY those traditions came into being is a different question, and includes many other factors.

General Discussion:
https://www.boundless.com/sociology/textbooks/boundless-sociology-textbook/culture-3/culture-and-adaptation-31/the-origins-of-culture-199-3031/
A Specific Example:
http://www2.psych.ubc.ca/~schaller/MurrayTrudeauSchaller2011.pdf