The AROTC program at Princeton is really good, that school also has a long history with the Army. The most recent CJCS (Gen. (Ret.) Mark Milley) was a Princeton grad. I am pretty sure they were also the only Ivy to not kick ROTC off campus during the Vietnam War. NROTC is also definitely doable at Princeton too, but a little more complicated because you have to commute to Rutgers for it.
Duke is a good school as well of course, I’ve heard the NROTC program is great there too.
I think it ultimately comes down to deciding which branch of service he wants to pursue and then comparing the two schools together. For example, Navy top choice for him? Narrow it down to Princeton NROTC vs Duke NROTC to make it easier. Also, definitely visit both schools during their admitted students’ days in April to help with the decision. During those days, get involved with/reach out to the chosen branch unit at the respective schools to get more of a feel for what life is like as a cadet/midshipman at Princeton/Duke. I know Princeton AROTC will set him up to stay with one of their cadets during Tiger Tuesdays (or whatever they call it now).