Both are great programs for voice. Oberlin is more widely known in the music world, and that “prestige” can translate into an advantage in auditioning for summer programs or in competitions. However, voice is a LONG road, and the most important thing in the first 4 years is developing solid technique --not getting roles in opera - (trust me, this is secondary). D is a MM2 and there are stellar students who went to places I had never heard of, getting big roles (which is the objective of the masters degree).
If the studios are equivalent in his mind, look at the fit and temperament of the student body. Where are his people? As a musician, he will spend a lot of time with his peers in ensembles and classes and have less free time than imagined. Even the music school within a university will be somewhat of an isolated bubble as the coursework in music is surprisingly time consuming. He should like the people he will spend most of his time with.
However, in my opinion the most important consideration after fit of studio is money.Having access to funds to use for summer programs, to travel to competitions, and to put toward living expenses in grad school is VERY important. Do not underestimate how much money you will spend outside of tuition on the VP path. Students can make a lot of great connections over the summer (usually starting summer after sophomore year), and this should be factored in financial planning. These programs help him identify teachers he may want to work with in the MM, and build his credentials. And save for grad school! Even if he gets good tuition scholarships as a grad student, living expenses in Boston, New York, LA, SF are high and could affect his ability to attend. IMHO, where you end up for grad school is more important with regard to prestige than where you are as an undergrad, as long as you are growing vocally and have solid technique. Best of luck to him!