G. Mark’s Answer
These are two very good, challenging and important careers. Comparing the two is not as simple as looking at annual salary. First, you can become a computer engineer with a four-year degree. Your masters degree will likely take another year. Becoming a dentist will take 7 to 8 years. There is more competition for spots in dental school, particularly because a computer engineer can generally enter a wider variety of positions in the working world. The other thing to consider is that being your own boss sounds very attractive, but running a business yourself is quite an undertaking. As a computer engineer, many of us can simply leave work at the end of the day and forget about it. Running your own business is a bit more taxing. Now, from personal experience, I can say that in many of my projects, I was responsible for the original invention and running the project until completion, so my weeks tended to be a lot more time-consuming than the average engineer, so there is significant variability.
Another thing to consider for starting your own practice is startup costs. Establishing a dental practice can cost 300 to 500 thousand dollars or more. And, like my own projects, you'll be responsible for your staff. As for salary, it's estimated that the average dentist makes in the 150 thousand range currently. Salaries for an accomplished computer engineer average approximately 120 thousand, with a bit more variability. Keep in mind that as a computer engineer, you'll typically be working for a company -- possibly a very large company -- that will bear the burden of overhead like office space, insurance, other benefits, etc..
Something to consider in becoming a dentist is that you do not necessarily exclude delving into computers. Computer engineering touches nearly every profession these days, so a dual undergrad degree has a lot of potential.
One thing to consider for each of these professions is that neither of them will be subject to automation anytime soon. They'll simply benefit from any technology advances. Both are lucrative and secure professions.