I can't quite put my finger on why I like some rap music but dislike the genre in general. It would be helpful for me to analyze what I like about each of the various rap groups that I do like to listen to, such as Jurassic 5 and the Roots. What is it about these particular groups that I find appealing that Ludacris and Busta Rhymes lack?
Perhaps All Music Guide is my friend here—a lot of classifications exist already for rap music. "Rap" is too broad of a category to help me decide what I like in the same way that "rock" is too broad. At first I thought that I liked hip-hop music and disliked rap, and thought of "hip-hop" as sort of just "semi-melodic rap." But that doesn't appear to be accurate. Most definitions I could find either said that hip-hop music was synonymous with rap, or that rap was a part of a broader culture known as "hip-hop," so it seems that the distinction I was using is flawed. I don't need names, but understanding existing classifications can be helpful in the same way that understanding known design patterns can be helpful to a software engineer even if they don't really present any new or outstanding ideas.
Of course, I don't like genres of music; I like pieces of music and individual artists: I don't necessarily like "classical music"; I like Beethoven and John Williams and Hans Zimmer. The same will be true for rap, and I think that this is going to make it harder to classify what I like about it, because the amount of rap that I like is so small compared to other genres. The argument can be made that it's irrelevant; that all that matters is whether or not the music is good, and that has merit. But, it would be nice to be able to better understand my own musical tastes.