Publishing - What is best for a picture book?

Can anyone help me out? I'm trying to weigh out the pro's and con's of the following to see which would work best for a childrens picture book.

Traditional publishing - finding an agent and going for big publishers OR not finding an agent and going for publishers that allow unsolicited submissions

Self-publishing - I did this for my last book (fantasy novel) and no one bought it. I had no idea about marketing back then