More locations: Now over THIRTY. More choices: special programs, volunteer positions, language classes. More security: Members of BBB, all courses externally moderated. More Accurate Info: No hand-picked testimonials, all course feedback availble online. More Support: worldwide lifetime placement assistance. More Experience-running worldwide courses for 10+ years. More FUN! ...... TEFL International
Much of my answer has already bee written. See my post from five years ago, in this thread.
Trying to decide between a TEFL Certificate and a CELTA is like trying to decide between 'a private jet' and 'a GulfStream'; the latter is a well-known type of the former.
Regarding working in Europe; Most EU counties give priority to employing EU passport-holders. With the UK exiting soon, there might be changes that mean getting a job if you're American is easier, but we'll have to wait and see.