I have written a few articles about Educreations and ShowMe, but have never really compared the two. They are both great apps on an iPad. Educreations and ShowMe are excellent tools for students to think out loud while working through math problems. They are also an awesome way for a student's teacher/coach to figure out what struggles a student is having while solving a math problem plus help students better their learning. The apps can also be a part of the final result to add voice to other creations from apps like Popplet Lite, Aviary, Skitch, or other similar creation apps.
Educreations is a tad better because you can create more of a slideshow effect and add photos from the web to the presentation/story with less dificulty than ShowMe. The other bonus of Educreations is that it can also be used on a computer through a browser. One thing to keep in mind is... once you start recording you have to finish and save or start all over again. There is no opportunity to edit something that you started using either application. I suggest creating one student account that all students log into. Then have the students put their initials on their work or in the title of their work. That way a teacher can log into one account and all of the ShowMes or Educreations are in one place.
I have pasted below a few student examples.