I have a BSEE from 81 (back when they barely admitted that computers were of any use at all, except to solve math problems) (but I took CS classes), and I graduated and took a programming job, and have been doing mostly software ever since (though the EE background has occasionally been useful.)
Recently, I've been taking some online classes to flesh out my computer science knowledge, and I've been finding the mathematical aspects substantially beyond anything I ever learned (discreet math, recurrence relationships, generator functions, OMG PROOFS, Set theory, statistics and magic numbers thrown around like they're second nature to everyone ("This is obviously the same as N choose M")) I mean, IIRC I took two+ years of various calculus and analytic geometry, plus the specific EE and Physics classes that used it and added things like phasors, but this CS-style math has me stumped!
Some schools are honest enough to separate "Computer Science" from "Computer Engineering." Yeah for them!
I think any of CS, CE, or EE, will earn you a comfortable living, but your major "success track" is to go into management, or play "startup roulette." :-(