I have no direct knowledge of the CFE beyond reading the link Joy shared with us, and of course as a part of the CQF faculty, I declare an interest.
It doesnn't explain how you can do the optional
C++, which is not something you could do without help, and there is no mention of tutorial assistance. Nor does it say who teaches, the CQF is big on that, enough that when at a recent information session someone asked (politely) who I was and why I thought I could teach
C++, there was a distinct change in the background noise.
Generally it does seem to cover a good subset of the CQF, but the order of topics doesn't feel right, for example Ito's lemma before convex functions ? or valuation of 2nd generation exotics before first order Greeks ?
But one can spend any amount of time arguing about the syllabus, certainly the CQF includes the result of some quite intense discussions...
I fret about the organisation issues that mugoyal cites, I've done various bits of my own education on a part time basis, and know how hard it can be to juggle with job, life et al even when the course is stable.
Organisation is a big thing in good course delivery, one that is easily overlooked. I have taught at various places, and sometimes that goes bad. For one firm I turned up at one place to do what was billed as a basic intro on a topic that was on the edge of my own skills. Every single guy in the room knew it better than me, and they had sent me to the wrong place as well. To cover themselves, they blamed me...
I teach a bit of Paul Wilmott's CQF, and it's very different.
It's hosted by 7City who are a pretty large training outfit, and they have a gang of people whose sole job is to make sure lecturers know where and what they are supposed to teach, there is surprisingly deep technical support, people who make sure the right notes are printed in the right number, etc. There's content management, and if I don't respond to the automatically generated nagging emails to make sure I turn up, more get sent. That sounds small, but most courses I know have had missed this, and students tell me how pissed they are, when you consider what each lecture costs. And of course all CQF lectures are recorded, which in my mind is essential for a part time course.
Also, if your life/work means you have to stop and restart, then you can join the next cohort with zero hassle.
I have no idea how much all that costs, but it will account for some of the difference in price between the CFE and the CQF.