I think the CQE is considered the "pinnacle" cert for the mathematical side, whether it be SS initiatives or SPC. The CQA is on the "standards" and procedures side, less math, more documentary. The O/E is a mix of both, but with less emphasis on the Engineering side and more similar to the auditing side. The O/E takes longer to get results from as well, since the first part is a timed essay, and this is graded by humans. I admit I resorted to bullet points on this one to make the time deadline (45 minutes I think), basically "pick a case study then detail what you would do to: x,y,z". By the time you read the cases (since you have to pick just one of three), and then reread the one you decided on, then formulate a response, time just disappears.
The CQE and CQM are really two different career paths, usually exclusive unless you are a glutton for punishment like me.