I like Ayumi Hamasaki. I have only heard a few of the songs, and out of what I have heard, I liked "Depend on You" the best. Come to think of it, didn't she do the ending song in Thousand Arms?
I do like Megumi Hayashibara better, personally. I'd say her best song would be... "Para Rira Para Daisu", well maybe not best, but I like that one. "Watashi wa ko neko" was pretty good too.