The two biggest differences between chemists and chemical engineers, however, are 1) chemical engineers are much more quantitative, whereas chemists are more qualitative; and 2) chemical engineers have an economic understanding that chemists usually lack.
1) While chemistry (along with physics) is more quantitative than many other sciences, there are still large areas within the field where you don't really need much more math than some high-level algebra. Organic chemistry, for example, is more concerned with understanding reaction mechanisms and can often care less about the details of how fast the reaction takes place. Chemical engineers don't worry so much about how a chemical forms, though, put are very concerned with how fast it forms, how much heat is evolved/consumed in the reaction, and yield.
2) A chemist's economic concerns pretty much start and end with "how much will it cost to do this experiment". Chemical engineers are trained to go much further. To give an example, let's say a company has two potential products in development, both of which will require the building of a new plant to produce. Product A is more expensive to produce, but the process is not too challenging and a plant could be on-line in less than a year. Product B offers a higher profit margin, but it requires the use of some exotic equipment that require two years lead time to purchase. The company cannot afford to build both plants, so it must decide which one to build. The engineer knows how to make that decision.
My tryst with chemistry was only after I joined IISc. I was fascinated by the materials synthesized by my colleagues in solid state chemistry unit (SSCU), whose building is opposite to the chemical engineering. Encouraged by the colleagues in this department, my students and I worked on using these materials as catalysts for various reactions. This has resulted in several joint students and publications and I have been most benefited by this association, which has finally resulted in me becoming an associate faculty in SSCU. Of course, CNR Rao, who founded SSCU, has been an inspiration and I was extremely delighted when he congratulated me on the Bhatnagar award mentioning that he got the award the same year I was born !