You called?
Stability is something that never reaches one as a quotient - you can always lose your job for no fault of your own. You can do stuff that makes that less likely; not sucking; working hard; not being a buzz-kill who moans; understanding when to try new stuff and when to just do what you are told. These are all things that generally get you past the first few rounds of firings.
Consulting is more stable than banks. Consultants advise on how to grow when times are good, and how to sort out a ****-storm when times are bad. Quotient of stability is nearer 1 there, though quotient of 'knowing where the f you will be next week' is nearer a zero.
IB - you can avoid one or two rounds of cuts by simply working clever. The third round, everyone is pretty good and it is luck and friendships that see you through. Banks have no issue with handing out pink slips when times are hard - it is central to their business model to cut like that and part of the game. Sometimes you are simply unlucky - ask 2008 MBAs who were toast because they never had a chance to learn their jobs.
PE / VC. For once, I will entertain this fantasy land where the tail of the distribution perhaps work. These are managing other people's money, so you are potentially victim of a cash call (several hedge funds with outstanding records closed last year because other funds blocked clients withdrawing funds, clients needed cash). If form is poor, you can't raise another fund. Goodnight Vienna. Stability? Well, given that the Feds are out to get you livelihood, I would say "minimal".
Marketing. Some day everyone is going to realize that marketing departments are about snake oil, much like human resources. Someone needs to explain spurious correlation to these folks and send them home. Until then - marketing is cyclical. Stability is a little better at Corporates, but you still run the risk that - like HP - mature firms raise margins by cutting costs. Marketing is a cost center.
As for working on Wall Street. Wall Street is full of people who want it - be "it" money, success, BSD status, Master of the Universe - there are seriously driven people. Driven to the extent that many wouldn't think twice about stepping on your head if you were all drowning. Not many places are like that, but then not many places give you quite the clear definition of how you are performing relative to your peer group.
You know pretty quick if you are done on an Associate program on Wall Street. First full year will give you a good clue (many will cut the bottom group then). Most will last a few more years with VP being the bit when the bank truly seperates the wheat from the chaf. Many leave by then as the idea of working extreme hours isn't as smart as they thought at school, in spite of everyone else telling them it was insane. You really have to be determined to do IB, or S&T or Research for that matter, as the first three years you are swimming through crap. Many can't stomach it. The market for jobs after that varies - if you have a solid reason to get out you could do well (kids or medical reasons I think work) as the bank may support you in your search. Otherwise, good luck and unlucky on making a big mistake.