@sc30coach
I am going to make a couple of assumptions that you can correct if wrong. First, I am assuming that you are probably looking at a total cost difference after 4 years of about $200,000. I presume that to attend WUSTL might involve some loans.
Second, I am assuming, as demonstrated by my presumption about loans, although this could still be true even if loans are not involved, that this $$ difference is not something that is trivial to your family, that it involves some level of change to the family lifestyle.
If this is true, and given your current desire for med school, I would have to recommend Barrett. The cost savings are just too high, and despite the difference in reputation you will still get a fine education at ASU. BME is tough everywhere. Now I certainly won’t tell you that your classmates, even within Barrett, will be as academically accomplished as your WUSTL peers would be. But a Barrett student isn’t like the average ASU student either, by a long shot. And within your major, after they weed out the chaff freshman year, you will be around a bright group, I have no doubt. And there certainly isn’t any reason you can’t have a fabulous time enjoying the other side of college life at ASU, who let’s face it are far more professional at that than WUSTL students could ever hope to be. So there is every chance you can have, if not the best of both worlds, at least an excellent balance between them.
FWIW, my D was potentially looking at a similar decision 6 years ago. She loved WUSTL, and she was impressed enough by Barrett and the low cost it would have been, to go ahead and apply after our visit there. She also got no merit from WUSTL and no doubt would have gotten no need based aid if we had applied for it. But in her case she also loved Tulane equally to WUSTL and they gave her a full tuition merit award, so the decision was easy. But she always said that she thinks Barrett would have been an interesting choice, with all the resources a large school like ASU has.
IMO, there is no school worth $200,000 more than Barrett, not even Harvard or Stanford. If you choose Barrett, I can tell you now you will always wonder what it would have been like at WUSTL, right up until you are paying $200,000 less for med school. Undergrad is still far more what you make of it rather than the school itself. By taking advantage of what Barrett offers, what the rest of ASU offers, and what the Arizona area offers (my D says one of the draws of Barrett was desert hiking and rock climbing) and maximizing that, you can do extremely well.