I'm also a non-native speaker with a little experience teaching children and I've just finished my CELTA. I dont have experience with TESOL but working for aninternational language school I have spoken to many people who have done it. Based on this I can say that they are not massively different. I personally found the CELTA VERY helpful. I learned alot in a short time and I feel that I had plenty of opportunity to practise my teaching and get feedback on it.
There was a variety of people of different backgrounds and experience in my course so I wouldn't say that it is for more advanced teachers. I would therefore recommend a CELTA. Its also pretty prestigious, being a Cambridge University certificate. As for the TESOL, it takes a slightly different appraoch with regards to teaching methods, but this is only a slight difference. So it may just come down to a price difference in the end.
A basic EFL job will usually require a degree and a TEFL/CELTA certificate. From a qualification point of view, I don't think they vary hugely.

Hope this was helpful.

Melissa
CELTA certified & teacher administration for Learnship Networks