Having to borrow $200K is crazy high for an undergraduate education. Heck, I always thought it was too much for doctors to graduate medical school with $200k in loans.
If the disparity were substantially less, then it may be an issue of penny-wise and pound foolish. Decades ago, I did forgo an opportunity to attend a lesser reputed college (also out of state) on full-ride(tuition, room/board, books/fees, travel) plus. I don't regret choosing the elite but my total debt was only a small fraction of the $200k facing the OP's DD. Were my kids to face the same choices, I might well nudge them toward the full-ride.