For my experience, I took web service exam first. Web service exam covers a little bit about EJB. Honestly, this exam is very stressful.
Now, I am preparing for EJB exam.
Web service exam covers some materials which may not be included in study guides (MZ's notes, Ivan's notes,
Java Web Service Up and Running, WSIT tutorial, J2EE version 5 and 6 tutorial, Ethuware mock exam, EPractice Lab, Jersey tutorial chapter 1-5 ...). You may want to google WS-*, for more supplemental materials.
This exam is overwhelming and it took me 14 months to study for it on daily basics.
It is hard to collect all the materials you want. And some materials are confusing and I needed to ask on this forum.
I wasted a lot of time struggling with some topics like Yahoo Rest service, J2EE core design
patterns, which are covered in those materials, but end up not in the exam at all.
One more thing is a web service exam has 12 questions about design and best practice. However, Oracle does not clearly specify what design and best practice will be on the exam. It is even hard for the mock exam publishers to guess.
But for EJB, everyone said reading JSR-318 (EJB specification), Frits's 101 pages of notes, Ivan's notes, Ethuware mock, the books recommended in this forum as well as EJB in action, are good enough to pass.
As I am reading Frits' notes, I have a feeling that this EJB exam will not be as tough as the web service one.