Probably depends totally upon what program you graduated from.
For me, my comp sci. degree covered a ton of different things:accounting, business, economics, programming, management, math, networking, web development, and a couple other things.
For my comp sci degree, the most math I had to take was algebra. In a college across town, the comp sci majors had to take about four semesters of calculus and another couple semesters of 300+ level math classes. The rest of their comp sci hours were done programming.
I can't comment on CE, because I have not gone through, or looked at any programs for it. I do believe though that CE requires in general, higher math and physics classes, as well as a lot of "engineering" classes that are not required for a comp sci major.
Soooo...to answer your question,
maybe
It depends upon three things:
1) job at hand
2) program you came from
3) competence level of applicant
In all honesty, a comp sci or engineering degree isn't even that important. Many people that I have worked with in the IT industry have all sorts of degrees such as literature, business, accounting, biology, and liberal arts.
The most important thing is how competent and skillful the person applying for the job is. All of my "job skills" were learned on my own, not in a classroom. Employers are so desperate for computer people, all they are requiring is a degree...they really don't care what it is in as long as you can do the job.
And any employer who blows off a job applicant because the person doesn't have a degree in CS, or CE, or CIS is just flat out ignorant and passing a very large percentage of skilled applicants.