To be clear, the question really is not should an author an author invest in either book marketing or book publicity, but rather, how much of each?
Book marketing covers sales and advertising, including things like speaking, book signings, website development, and handing out fliers.
Book publicity covers the media, both traditional media (TV, radio, print, online) and social media (blogs, podcasts, FB, Twitter, LI, Instagram, You Tube).
You need not to choose one over the other but to be involved in both – in big quantities of time, money, and effort.
Even though I’ve been involved in promoting authors and books to the news media for nearly 30 years, I will state that book marketing may be more important than PR. However, to succeed at selling your book, you’ll need some help from the news media.