I think the bigger challenge is to convince the child to let go of the brand name school in favor of a full ride. I have seen several cases where the decision has gone in favor of full ride and others where the brand name school won.
It all depends and it is an entirely personal/family decision in my opinion. In the long run, there are countless factors within and outside our control to define and determine success. I don’t believe in the averages and the stats as a justification to attend one school over the other.
If the cost is tremendous financial undertaking as you stated, I think the child will automatically make the right call and go with the money.