There are a couple of primary differences between the KJV and the “Catholic” Bibles of today. I’ll use the New American Bible (NAB) as the point of comparison since it is the translation read in English speaking American Catholic churches today.
To begin with, most KJV Bibles have 39 books in the Old Testament, all originally written in Hebrew. However, the Old Testament of the NAB contains 46 books, including an additional seven (Tobit, Judith, 1 & 2 Maccabees, Wisdom, Ecclesiasticus, and Baruch) which were part of an ancient Greek translation of the Hebrew Bible. These seven books are variously referred to as the “apocryphal” or “deuterocanonical” books and are usually placed between the Old and New Testaments. In this sense, it can be said that Catholic Bibles have more books in them than Protestant Bibles (here represented by the KJV).
The other primary difference between the two is one of translation/textual accuracy. The KJV was translated more than 350 years ago; the NAB just in the last few decades. Translators of the NAB took advantage of ancient manuscripts that were discovered since the introduction of the KJV, and using these they arrived at a text believed to be closer more consistent with the original manuscripts of the Bible.
I always suggest that people feel free to use whichever translation most resonates with them for their prayer and meditation – the primary message of God’s love expressed to us by Jesus is unadulterated. However, for academic study, the NAB is a better bet.