Valz, there are many good resources. And by the way, if you pick up an old KJV it also has the "full of grace" in Luke. "Favored one" is a very new translation.
Basically, Douay-Rheims is an old translation of the Latin Vulgate. The Latin Vulgate was the first Bible written in vernacular. It was translated from Greek and Hebrew texts by St. Jerome.
The KJV used old Greek and Hebrew texts, as well as the Latin Vulgate, and it's not a terrible translation, but has some problems that the Douay Rheims translation does not. First of all, it was specifically written for poetic rhythm. Translation was fudged according to what rhymed better, and made for more beautiful prose. This is highly evident if you compare Psalm 23 between the texts. The Douay Rheims made no effort to rhyme or have rhythm, but simply be as accurate a translation word per word. Second of all, the KJV was translated at a time and place in history where the oppression of the poor, as well as oppression of women was rampant. Some of this skewed the KJV in favor of the rich men who were involved in it's translation.
You can find a great deal of information about Catholic bible studies at Robert Sungenis site: www.catholicintl.com
His links page has many links to different bibles online for comparison.