It looks like the CELT is accredited by the Irish Department of Education, while CELTA is accredited by University of Cambridge ESOL Examinations. TEFL is not necessarily accredited, but may be by a company such as Accet. This is one reason why TEFL certification is generally seen as being of lower or dubious quality, so for me it was important to list my certification as "+150 hour, Accet accredited" for certain employers. I don't know how you plan to use yours, but I'd recommend getting a YL (young learner's) extension. Most newly minted teachers get gigs teaching kids because employers tend to see teaching kids as "easier" (it's not, if you're doing it right). Anyway, right off the bat, you'll be getting a higher salary (if the employer is worth their salt, which honestly, a lot of them are not). Anyway, with that credential it's easier to get a good paying job in a decent location.
Thanks for the tip! That might be a very good idea - I've already heard that new teachers are usually assigned young learners.