Hello Mike Smyth,
Welcome to CodeRanch!
Firstly, as per you've mentioned, much of your experience is in Core Java and Swing - not in JEE. In that case, I would suggest not even to think about OCMJEA. Even if you think you can crack the exam, I would suggest to wait till JEE 6 version of the exam comes out. IMHO, its simply not worth the efforts and expenses to give such a big exam for outdated version of JEE.
Secondly, I would highly suggest to go for OCMJD (especially when you don't have to shed money for mandatory course - it seems that your employer would be bearing the expenses

). But again, if you have any plans to got for JEE in future, then by all means, go for EJB exam. This is because, you've already got a decade of experience in Swing. OCMJD is nothing fancy compared to that. Secondly, why to certify yourself in something you might not use in future? At your stage of experience, I think JEE certification is better option.
But again, those certifications are quite cheap - so just give it a though - if expense is the thing which is stopping you from giving OCMJD, then well, you got a chance now

However, if you know the future of your project, and have any idea about core knowledge about threading is not gonna be much of a selling point, then JEE is the way to go (I'm saying this especially because OCMJD contains nothing fancy that someone with 10 years of experience has not seen in his/her career).
I hope this helps.
All the best.