The KJV was officially a revision of the 1568 Bishops' Bible. Thankfully, the KJV did not follow some of the Bishops' Bible poorer renderings, but instead followed some better renderings in the Geneva Bible.
The 1560 Geneva Bible could be said to have this advantage over the KJV: the fact that the Geneva Bible was not influenced by the Roman Catholic Rheims N. T. while the KJV was influenced by it. The KJV took or followed some words used in the Rheims.
Church of England Archbishop Matthew Parker, who directed the making of the Bishops' Bible, would not permit the printing of the Geneva Bible in England for several years. Archbishop Parker was also involved in having some of the translators of the Geneva Bible persecuted. After Parker's death, the Geneva Bible was printed in England a few years until its printing was again
stopped around 1618. In the 1630's, Archbishop
William Laud would make the binding, selling, or
importing of the Geneva Bible a high commission crime. Even with all this governmental suppression and opposition by the Church of England, the Geneva Bible is said to have remained the most popular and beloved English Bible up to the 1640's or later. Some scholars claim that the KJV did not became the Bible of England until the restoration of the monarchy in 1660.
While the KJV may have improved some renderings in the Geneva Bible, there are at least a few places where the Geneva Bible could be said to be clearer, better, or more accurate than the KJV.