It is all about the syntax of the question. It is only necessary to prove that it is possible (i.E. "can") for an individual (i.E. "one") to serve society better... In this context, there exists any number of folks who, if they became doctors, would likely kill a portion of society. Among these "killer doctors" there must exist at least one who would not kill any portion of society by becoming an engineer; perhaps a computer engineer. Of course, if the question were asked in reverse (doctor rather than an engineer), the answer is also yes.
Modern doctors are becoming heavily reliant on technology, and for good reason. Diagnosis, treatment, and patient care have made significant leaps in accuracy and effectiveness during the last 2 decades due to the booming medical device industry. Have modern doctors improved as well? Certainly, but their improvements are far less game changing compared to the modern world of medical devices. Medical imaging and diagnosis of diseases can be as easy as identifying two different colors or reading a numerical value... Surgeries can be done by a pre-programmed robot, and most modern medical devices can be operated by pressing a sequence of two or three simple buttons (e.G. Stenting , embolization of aneurysms). Cancer treatment? Non-invasive laser therapy. Bottom line is doctors will forever be necessary and critical in this world, but their impact in the innovation of their own field and the health of humanity, as of right now, is being severely dwarfed by biomedical engineers. Will this be true in the future? Who knows? That depends on the drive, talent, and passion of the current generation of engineers and doctors.
A person can serve society better by becoming a lot of different things. The key is to find the skills you are best at and use them. If you don't have the skills to be a doctor than becoming a doctor is not going to help society at all. You should do your best for society.
Medicine is no longer just in the real of doctors anymore, and an increasing number of medical procedures are heavily reliant on computers and medical devices. Engineers can help people in the same medical way as doctors in the near future, in addition to a number of other potential fields.
Whether one is a doctor or engineer, one can serve society. Doctors, however, keep disease at bay and treat illness. Without them, human beings would cease to exist, and there would be no reason for engineers to design and build. In order to keep society going, we must have doctors.