- Chemists suffer greatly from the fracturing of their subject. Chemists, particularly those with an advanced degree, are not just "chemists", they are analytical chemists or organic chemists or ... while chemical engineers are just chemical engineers. Without that limiting adjective in front of their major, ChemE's are not already pre-fitted into a box that may handcuff you for life. It is extremely difficult for an analytical chemist to get out of that field and into say, a product development job . In contrast, I knew a ChemE in grad school who studied surface catalysis the whole time, yet found a job as a polymer engineer. Again, he was a chemical engineer, not a catalytic chemical engineer, and people just see that as being more flexible.
- ChemE's in grad school don't face that dreaded attitude of "if you don't become a professor, you're a failure" that chemists often do. Most of them enter grad school planning to work in industry anyway. And for those that do decide to stay academic, the need to do a post-doc, let alone multiple post-docs is just not there, probably because the competition for the jobs just isn't there either.
- But lastly, no matter how good the potential jobs are, don't go ChemE if you hate math. You'll need a lot of it, not only required math classes, but then you'll use it all in fluid mechanics, control theory, reactor design...Same with thermodynamics. There's the stuff you get in general chem, then the P-Chem classes, and then also a chemical engineering specific class. And maybe another class if you go to grad school.(O.k., the math issue get covered plenty - I just want to reinforce it as it is quite true.)
This is what I've seen over the last 20 years or so, in a generalized fashion. Hopefully it is good food for thought to anyone thinking about the chemistry/ChemE choice. I've been fortunate to be what we used to call a "big C" ChemE, while most of my colleagues are "big E" ChemE's. As such, I've been able to still spend time in the lab playing organic chemist. It's actually pretty uncommon and I freak out a lot of people (both chemists and ChemE's) with how much chemistry I know. (Both groups expect me to know a lot less.)
 For background, I majored in Chemical Engineering, getting my Bachelor's from Minnesota and a Masters and Ph.D. from Illinois. I did attempt to do a double major at Minnesota in Chemistry as well, but couldn't pull it off due to scheduling conflicts - the last class of Inorganic was at the same time as my Control class and both were required to graduate, so a choice had to be made.
 I will be up front that it will be full of generalizations and stereotypes, so if that bothers you, stop reading now. The fact that generalizations and stereotypes both exist and even have words to describe them says that humans are both prone to using them and that there is some truth to them. I consider them the same way I look at averages - you have a range of data and the average gives you some idea of what it is like. Somehow people are very comfortable with working with averages - too comfortable if you ask me as too many seldom look past them to even see a standard deviation - but somehow never see that a stereotype is just an average. Instead, stereotypes are considered to be as bad a racism, an entirely different concept.
 Trust me, I know. My wife made that transition. It was not easy. First she had to find a hiring manager willing to take the risk, and then once hired, gain acceptance from colleagues who continued to place her in the analytical chemist box.