Well, I think those two approaches are complementary.
Greenpeace released the documents and left the discussion of specific problems within them to others, such as citizens rights movements and journalists.
EFF just happens to be one such party which specializes in digital rights, so it is only natural that they look at the papers released by Greenpeace, and pick the worrying parts within their domain of expertise up for discussion.
It is up to each citizen to decide which of the issues within these documents, brought up by journalists and others he cares deeply about.
But I think many people might just end up saying, "yeah EFF, that is bad stuff, but there is worst stuff in this treaty which I'd rather focus on".
I think the approach Greenpeace Nederland took was better. They didn't try to force the discussion to be only about issues they cared about.