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Kheenbish
Degree for the Army ROTC program doesn't make a difference, aside from those in what are called STEM degrees (Science, Technology, Engineering, and Math). STEM offers those cadets special scholarships as there is a higher need for individuals with those degrees as well as an increase in Order of Merit List points during accessions the third year. for Science and Math majors currently it's a .5 increase on the OML point totals and a 1 point increase for Engineering and certain Technology related degrees. It's hard to tell what that really means, but relative to the OML that usually turns out to be a lot as a mere point can make the difference of over 200 other cadets in the program during accessions.
As for other degrees, there really isn't much difference. Another I can say makes a difference on the OML is only any Foreign language related degree because foreign languages get up to 2-something points overall but that's only because it's counted for each semester a FL class is taken, so the total compounds over 4 years.
Some branches do indeed reserve a certain amount of slots for people with certain degrees. I don't know the percentages exactly, but from FY13 I do know there was 50% slots reserved in Engineering for Engineering majors and 50% reserved in Signal for a variety of different majors, such as MIS. I don't know that list, but the number of majors for that was pretty substantial. Others that reserve 50% slots for certain majors are Chemical and Ordinance..