Depends on what you want. It doesn't matter "who has priority" when it comes to learning the subject. Pearl's book is good, but one big disadvantage of reading just Pearl is Pearl does not deal with the statistical inference end of causal inference very much (by choice). Actually, I heard Pearl has a new book in the works, more suitable for teaching.

But ultimately we must draw causal conclusions from actual data, so statistical inference is important. Some big names that combine causal and statistical inference: Jamie Robins, Miguel Hernan, Eric Tchetgen Tchetgen, Tyler VanderWeele (Harvard causal group), Mark van der Laan (Berkeley), Donald Rubin et al (Harvard), Frangakis, Rosenblum, Scharfstein, etc. (Johns Hopkins causal group), Andrea Rotnitzky (Harvard), Susan Murphy (Michigan), Thomas Richardson (UW), Phillip Dawid (Cambridge, but retired, incidentally the inventor of conditional independence notation). Lots of others.

I believe Stephen Cole posts here, and he does this stuff also (http://sph.unc.edu/adv_profile/stephen-r-cole-phd/).

Miguel Hernan and Jamie Robins are working on a new causal inference book that is more statistical, might be worth a look. Drafts available online:

http://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/