Applicant to place ratio is such a bad way to determine competitiveness. You could have a really high applicant to place ratio if your course is a really popular backup course. For example: If lets say your course is very popular as a backup (presumably because its easier to get in), a lot of people will apply. The program accepts a lot of people but very few choose to go because they got into their preferred choice. You end up with a very high applicant to place ratio.
On the other hand, if your course is not so popular (high self-selection rate), not many people apply. However, it is the 1st choice for many. In the end you will have a very low applicant to place ratio. A good example is Oxbridge medicine. Oxbridge medicine has a 6 to 1 applicant to place ratio, whereas nearly every other medicine course has a higher one ranging from 7 to 1 to 12 to 1. However, over 90% of those given an offer by Oxbridge end up taking that offer. So really applicant to place ratio is not a good indicator of a program's competitiveness.
A much better indicator is acceptance rate. i.e. number of applications: number of offers used in conjunction with matriculation rate i.e. number of offers:number of spots. A low acceptance rate and a high matriculation rate indicate a very competitive program.
To answer the post, there are many competitive degrees. I would offer medicine as a degree that is competitive across the board.