My thoughts are to drill deeper.
I'll start with program B - Many losing programs bring in a new coach who, of course, claims he will turn the program around. What are the real chances that this is the guy? It usually doesn't turn out that way. Playing is great. Playing for a perennial loser and getting hammered regularly can take the joy out in a hurry. Do you see indicators with this guy, beyond his required dialog, that lead to believe maybe he can turn it around? What is his relevant background? Can he recruit strongly at this level in this region? Can he win at this level once he does so? What do the other recruits look like? Are they clear upgrades, game-changers? (I'm guessing the answer is no since you say they are likely to continue taking a beating for a while) Agree with others that the ultimate scenario is to come in and be part of turning a program around. But, that sounds like it's still a big IF here. Try to dig deep to figure that out.
Program A - It's always great to be part of a winning tradition. And, there are many rewarding experiences that come with the process of earning playing time over the course of a year or two before hopefully earning starter status. But, again, honest assessment has to come into play here. Many successful D3 programs are good because they are constantly filling the pipelines with good players. As you pointed out, there is no athletic scholarship and there are no roster limits. So, it is very common dialog for a successful D3 coach to say a player may get some PT but mostly spend a year or two developing before earning starting time with his coveted program. There is nothing to lose and no real commitment to put that player in the position to actually do so after a year or two. In fact, he will be constantly working hard to protect his winning reputation and find better players than your son. That's his job. So your player has to do some serious evaluation of what his realistic chances are to get that playing time and, eventually, that starting opportunity. If he believes he has a real shot, knowing that the HC will continue to bring in good players, I think this is a great option.
Two good academic choices, among others, is a great problem to have... congratulations to your son!