I think paperstars has a point there. They are very different courses leading to very different lifestyles. Don't be put off by some this "my friends has a 2.1 from .... and can't get a job", I graduated this year with a 1st Class MEng but I was offered a graduate job 2 years ago after completing my placement. I have friends that got a 2.1 and 2.2 and they also have god Chem Eng grad jobs. It is important that you pick what you're interested in as it is you that will have to attend the lectures and sit the exams. I can tell you first hand that it is not easy and it will challenge even the most intelligent, as will medicine.
One of the main differences is biology. You must be very good at it to be a Doctor but it's not the main focus of the Chemical Engineer, although you must have an understanding of it in the context of biomaterials and energy and products from biomass etc. Other than that, you must be able to deal with blood, open wounds and the like to be a Doctor. Sounds silly but you'd be surprised at the number of people that turn up without first considering that.
In summary, both are good in my opinion so long as you're good at them. If you don't think analytically and enjoy problem solving then Engineering (of any sort) is not going to be your best choice, if you don't like medicine and all that goes with it (including public service) then you won't make a good Doctor. People tend to enjoy what they are good at and tend not to enjoy what they are not good at, worth keeping in mind when considering peoples opinions (including mine). Good luck