Quelli is a pronoun, which means it stands by itself. It's masculine plural.
Quegli is an adjective, also masculine plural, but it's used before s + a consonant or z.
This may be helpful. http://www.unilang.org/course.php?res=71 (Lesson 3)
I read the link that Viaggatore provided, and in reading the definitions associated with this adjective, I am getting the impression that it does not mean "well-liked", but rather "widely-used". Is this correct?