我没有最喜欢的：there's nothing I like the best. / I have no favorite. 我不喜欢的：(sth. that) I do not like. 我喜欢很多电影，但是没有最喜欢的。 I like a lot of movies, but there's no one I like the best. 我喜欢很多电影，但也有很多是我不喜欢的。 I like a lot of movies, but there're also many movies that I don't like.

"我没有最喜欢的"means there is nothing I like best,"我不喜欢的"means something I don't like.For example,我没有最喜欢的食物=There is not any food I like best.我不喜欢的食物是面包=The food I don't like is bread.If you show the situation where these two terms are in,it will be easier to explain.

没有最喜欢的，只有更喜欢的。。 我不喜欢的有人，有物。多拉。。 人生~

我爱运动，我不喜欢懒散不！or I love sports, I do not like slackers!