The Coverdale Translation and the Great Bible were both the work of Miles Coverdale. To the best of my knowledge Coverdale relied heavily on the works of other translators, especially William Tyndale.
This raises the question in my mind whether his translation of the Bible was actually done from original Hebrew and Greek manuscripts or if he relied on the works of previous translators as his source material.
This article seems to indicate the original languages were used:
The "Great Bible" Printed in 1539 AD: The First English Language Bible Authorized for Public Use (80 Books). It has the following disclaimer: The Bible in English, that is to say the content of all the holy scripture, both of the old and new testament, truly translated after the verity of the Hebrew and Greek texts.
However this seems unlikely given that the Catholic Church had banned translations except the Latin Vulgate for 1000 years. Is there actual evidence that Coverdale made his translation from original Hebrew and Greek scriptures or was the Latin Vulgate his source?